President Trump got through the entirety of the first general election debate without telling the American people what he would do in a second term.

Instead Mr. Trump delivered a performance that amounted to shouting his Twitter feed at former Vice President Joseph R. Biden Jr. while Mr. Biden was speaking. He yelled about entanglements involving Mr. Biden’s son Hunter, accused him of being in league with antifa and socialists, and said the federal government’s top scientists were wrong to be cautious about a coronavirus vaccine.

It all served to keep the presidential campaign about Mr. Trump’s conduct in office, a proposition that to date has left Mr. Biden with a sizable lead in both national polls and surveys of key battleground states.

At no point during the debate did Mr. Trump pivot away from his personal grievances with the news media, with the moderator, Chris Wallace, or with Mr. Biden.

Even at the debate’s close, after Mr. Biden delivered a plea to the American people to vote and a reminder that voters alone will decide the election, Mr. Trump ranted about perceived slights cast upon him by the Obama administration during his 2016 campaign and said he would ask the Supreme Court to “look at” ballots cast in the election.

With just five weeks to go before Nov. 3, Mr. Trump needed a debate performance that shifted attention in the campaign from his performance in office to Mr. Biden’s vulnerabilities, be they his lengthy record in the Senate or his occasionally unsteady moments on the campaign trail.

But instead the debate demonstrated what voters — even Mr. Trump’s own supporters — have said they dislike about the president: his impetuousness and inattention to solving problems like the coronavirus crisis that have directly affected people’s lives.

Mr. Biden, on the other hand, took several opportunities to speak directly to the American people, looking directly at the camera and gesticulating to viewers at home. He addressed them directly — with statements like, “I don’t trust him at all, nor do you, I know you don’t” — and implored them to vote.

President Trump dramatically escalated his effort to undermine public confidence in the integrity of the election at the first presidential debate, urging his supporters to “go into the polls” to shadow Democrats — while suggesting he was “counting” on a conservative Supreme Court to determine the victor.

Mr. Trump’s statements came at the end of an ugly 90-minute debate, and at the end of a rambling string of false and familiar claims that Democrats are using voting-by-mail procedures as a way of stealing the election from him.

The high court needs to “look at the ballots” in the presidential election, Mr. Trump said.

The extraordinary request came before most of the voting has even taken place. The president even revived his 2016 rally cry that the election was already “rigged,” despite the absence of evidence of widespread, or even sporadic, wrongdoing.

“This is going to be a fraud like you’ve never seen,” Mr. Trump said. “We might not know for months because these ballots are going to be all over.”

Mr. Biden, who had previously delivered a plea to voters that Mr. Trump “cannot stop you from being able to determine the outcome of this election,” turned to the camera and said: “He’s just afraid of counting the votes.”

Mr. Trump’s comments come just days after he told reporters at the White House that he would not commit to a peaceful transfer of power if he is to lose the election, and were followed by Mr. Biden’s assurance he would abide by the results of the election once all the votes were counted.

Later, Mr. Trump touted his support for efforts by conservative groups to congregate at polling places frequented by Democrats — a move that has been denounced as a campaign of voter intimidation at a time when Mr. Biden seems to be widening his lead in several key battleground states.

“I’m urging supporters to go into the polls and watch very carefully. Because that is what has to happen. I’m urging them to do it,” said Mr. Trump.

He went on to falsely accuse officials in Philadelphia of preventing his supporters from monitoring electoral activities this week; In fact, the officials turned some of Mr. Trump’s backers away because they had not registered as poll workers.

”There was a big problem today in Philadelphia they went in to watch. Poll watchers. A safe thing. They were thrown out. They weren’t allowed to watch,” he said. “Bad things happen in Philadelphia.”

The exchange was merely the latest effort by Mr. Trump to cast doubt upon election results. He has for years made false claims about voter fraud. Even after he won the 2016 election, he said without evidence that millions of illegal votes were cast for Hillary Clinton. Mr. Trump even convened a White House commission on voter fraud, which disbanded in 2018 without having uncovered evidence of illegal votes.

In recent months, as his standing in the polls has fallen, Mr. Trump has pre-emptively argued that Democratic elections officials are orchestrating a scheme to send extra mail ballots to like-minded voters. There is no evidence of this.

President Trump refused to categorically denounce white supremacists on Tuesday night, diverting a question about right-wing extremist violence in Charlottesville, Va., and Portland, Ore., into an attack on “left-wing” protesters.

“Are you willing tonight to condemn white supremacists and groups to say they need to stand down and not add to the violence and number of the cities as we saw in Kenosha and as we’ve seen in Portland?” Chris Wallace, the moderator, asked the president.

“Sure. I’m willing to do that,” said Mr. Trump, quickly adding, “Almost everything I see is from the left wing. Not from the right wing.”

When Mr. Wallace pressed on, the president asked, “What do you want to call them?”

“White supremacists,” the moderator replied.

“Proud Boys — stand back and stand by,” he said, apparently addressing the far-right group. “But I’ll tell you what. I’ll tell you what. Somebody has to do something about antifa and the left. This is not a right-wing problem. This is left wing.”

Mr. Trump highlighted left-wing violence when asked to condemn white supremacists, despite racist extremists’ committing more lethal attacks in recent years. Kenneth T. Cuccinelli, the acting deputy secretary at the Department of Homeland Security, said days later that “when white supremacists act as terrorists, more people per incident are killed.”

When Mr. Wallace pointed out that Mr. Trump’s own F.B.I. director, Christopher A. Wray, had said that antifa is an idea, not an organization, the president replied, “You have to be kidding.” (The director also said this month that “racially motivated violent extremism,” mostly from white supremacists, has made up a majority of domestic terrorism threats.)

The exchange came after a rambling discussion about law enforcement and protests.

Mr. Trump, under fire for his handling of the coronavirus crisis, has tried to turn the election — so far unsuccessfully — into a referendum on Joseph R. Biden Jr.’s reaction to the protests and sporadic street violence that came after the killing of George Floyd in police custody.

From the earliest days of his presidency, Mr. Trump has repeated falsehoods about the national murder rate and has seized upon outbreaks of violence in American cities to make the case that Democrats are unfit to lead.

Mr. Biden has tried to walk a narrow political line, expressing support for the aims of peaceful protesters and the Black Lives Matter movement while repeatedly expressing his disapproval of violence.

“Burning down communities is not protest,” he said last month during a visit to Kenosha, Wis., where Jacob Blake, a Black man, was shot multiple times by the police with his children nearby.

Mr. Trump’s strategy does not seem to be working beyond his base. Recent polls in battleground states have shown that most voters view the protests as justified. And a recent Quinnipiac University national survey of likely voters found that only 35 percent felt Mr. Trump could make the country safer.

 

Members of the Proud Boys, a far-right group that has endorsed violence, celebrated on Tuesday night after President Trump mentioned them during the first presidential debate.

Asked whether he condemned white supremacists and military groups, Mr. Trump demurred and then said, “Proud Boys — stand back and stand by.”

Within minutes, members of the group were posting in private social media channels, calling the president’s comments “historic.” In one channel dedicated to the Proud Boys on Telegram, a private messaging app, group members called the president’s comment a tacit endorsement of their violent tactics.

In another message, a member commented that the group was already seeing a spike in “new recruits.”

Mr. Trump’s rival, Joseph R. Biden Jr., noted that the group was celebrating Mr. Trump’s remark, pointing in a retweet to some of the comments being made.When asked what Mr. Trump meant by “stand by,” Jason Miller, a senior adviser to the president’s campaign, said it was “very clear he wants them to knock it off.”

The Proud Boys describe themselves as “a pro-Western fraternal organization for men.” The group has openly endorsed violence, and has recently been tied to several violent incidents at recent protests.

The Proud Boys were formed in 2016 by Gavin McInnes, one of the founders of Vice Media. Mr. McInnes said in an interview in November 2018 that he was “quitting” the Proud Boys.

Several civil rights groups have condemned the Proud Boys, including the Southern Poverty Law Center, which classifies them as a hate group, and the Anti-Defamation League, which refers to them as “hard-core white supremacists.”

Twitter suspended the Proud Boys from its platform in August 2018, and Facebook followed with a similar ban in October 2018. In the years since, the group has continued to expand its numbers on other social media platforms, and has become more visible at protests.

 

Despite an extraordinarily contentious first presidential debate, Joseph R. Biden Jr.’s campaign pledged late Tuesday night to participate in the remaining two televised showdowns.

“Joe Biden’s going to show up,” Kate Bedingfield, a deputy campaign manager, said on a conference call with reporters after Tuesday’s debate in Cleveland. “He’s going to continue speaking directly to the American people.”

President Trump, she added, “hasn’t shown up for the American people once since he became president, and we’ll see if he decides to show up in Miami next month.”

Tuesday’s debate saw the president routinely interrupting Mr. Biden and Mr. Biden openly mocking Mr. Trump, leading some observers to wonder if there was anything to be gained in going ahead with the second presidential debate, which is scheduled for Oct. 15 in Miami.

That debate will have a town-hall-style format with questions from Miami-area residents.

“There is an open question here, based on what we saw from Donald Trump tonight: Is he going to try to bully actual voters?” Ms. Bedingfield asked.

She acknowledged that there were “ongoing discussions” about the rules and format for the debates, and said she imagined there would be “some additional conversations.”

“But yes,” Ms. Bedingfield added, “we are committing to attending the debates.”

Also on the call, the Biden campaign said it had raised $3.8 million between 10 p.m. and 11 p.m. Eastern time, as the debate aired. The campaign’s digital director, Rob Flaherty, wrote on Twitter that it was the campaign’s best hour of online fund-raising “of all time.”

 

With a pugilistic President Trump relentlessly interrupting his opponent, Joseph R. Biden Jr., Chris Wallace of Fox News, the debate’s moderator, repeatedly struggled on Tuesday to keep the proceedings coherent, reduced at times to pleading with the president to pause and allow his opponent to speak.

“Mr. President, I am the moderator of this debate, and I would like you to let me ask my question and then you can answer it,” Mr. Wallace, sounding more headmaster than moderator, instructed Mr. Trump early on. (Mr. Trump did not accede.)

In a brute-force style, Mr. Trump flouted the agreed-upon ground rules and refused to allow Mr. Biden his two minutes to respond to questions, leaving Mr. Wallace yelping at one point, “Let him answer!”

Not satisfied with merely speaking over his Democratic opponent, Mr. Trump took aim at the moderator, too, repeatedly scolding Mr. Wallace. “I guess I’m debating you, not him, but that’s OK, I’m not surprised,” Mr. Trump said after one query from Mr. Wallace he disliked.

The debate had no breaks. But at the midway point, perhaps sensing that Mr. Trump was threatening to steamroll the event, Mr. Wallace did something unusual for a presidential moderator: He effectively called the debate to a temporary halt.

“The country would be better served if we allowed both people to speak with fewer interruptions,” Mr. Wallace said, directly asking Mr. Trump to yield a higher civic ideal. “I’m appealing to you, sir, to do it.”

“And him, too?” the president replied defiantly, nodding at Mr. Biden.

“Well, frankly, you’ve been doing more interrupting,” Mr. Wallace replied.

 

The country has never seen a debate like the one it saw Tuesday night. From the shouting and interruptions — mostly from President Trump — that made it almost unintelligible at times, to Mr. Trump’s call-out to the Proud Boys, here is what some political commentators thought.

By far the most discussed moment was the one in which President Trump refused to condemn white supremacists.

“The refusal of the President of the United States to denounce white supremacists on nationwide TV when asked to do so directly, launches us into a new and very, very ominous place.” — Sherrilyn Ifill, president of the NAACP Legal Defense and Educational Fund, on Twitter

“He wouldn’t say he condemned white supremacy. He wouldn’t say he condemned white supremacy. He wouldn’t say he condemned white supremacy. He wouldn’t say he condemned white supremacy. He wouldn’t say he condemned white supremacy.” — Amanda Renteria, board member of Emerge America, which supports Democratic women, and former national political director for Hillary Clinton, on Twitter

In an extraordinary remark on CNN, former Senator Rick Santorum of Pennsylvania blamed the moderator, Chris Wallace, for Mr. Trump’s call-out to the Proud Boys.

“He was asking the president to do something that he knows the president doesn’t like to do, which is say something bad about people who support him.” — Rick Santorum, who subsequently acknowledged that he was referring to white supremacists

More broadly, commentators remarked on the aggression of Mr. Trump’s approach.

“Not only was this Trump engaging in spectacle. This was spectacle on steroids. It was a clear display of aggressive masculinity meant to mobilize and appeal to white male voters.” — Anna Sampaio, professor of ethnic studies and political science at Santa Clara University, on Twitter

“Trump was also nasty and crazy towards Hillary in the 2016 debates, but he had a discernible message — on being an outsider, on immigration, on corruption. There was absolutely no argument from Trump tonight, just arguing.” — Jon Favreau, a former speechwriter for President Barack Obama, on Twitter

Many expressed disgust at the chaos of the debate, and there were some calls for Mr. Biden to refuse to participate in subsequent ones. (His campaign rejected those calls.)

“A hot mess inside a train wreck inside a dumpster fire.” — Jake Tapper, a CNN host

“As a political matter Biden did fine, and Trump hurt himself. But for the sake of the country Biden should consider refusing to do any more such ‘debates.’ Biden can do weekly town halls, including Trump supporters. But he shouldn’t dignify Trump by being on stage with him again.” — Bill Kristol, editor at large of The Bulwark and “Never Trump” conservative, on Twitter

“We need to hear tomorrow from the Presidential Commission on Debates. They must outline a plan for how this is going to work going forward including cutting off mics for interrupting. 2020 is far too important to have two more episodes of that. Because that was not a debate.” — Robert Gibbs, former White House press secretary for President Barack Obama, on Twitter

Few thought the debate would change the race substantially.

“Trump is behind & needed it more. conservative media will make use of some Biden speech patterns. But Trump bullying was obvious & confirmed by Wallace. Biden mobilization message could also cause instant ballot requests/returns.” — Matt Grossmann, director of the Institute for Public Policy and Social Research at Michigan State University, on Twitter

 

President Trump, heckling and taunting, tried to tear down Joseph R. Biden Jr. on Tuesday night.

“China ate your lunch, Joe,” he said at one point. When Mr. Trump tried to bring up the issue of Mr. Biden’s troubled younger son, the Democratic nominee did what he showed up to do: Try to stand above the fray and appeal directly to undecided voters exhausted by the past four years.

“His family, we can talk about all night,” Mr. Biden said. “This is not about my family or his family. It’s about your family.”

Coming into the debate, the candidate onstage who needed a reset was Mr. Trump, not Mr. Biden, who simply needed to hold onto his polling lead and offer up a counter model to voters.

Mr. Trump, interrupting throughout the debate, appeared aggressive and assertive, at one point challenging Mr. Biden to name law enforcement groups that had endorsed his campaign. The president also claimed that antifa would overthrow Mr. Biden.

“It’s hard to get a word in with this clown,” Mr. Biden said.

The president’s performance is likely to please members of his base, who saw the entertaining, loudmouth fighter onstage whom they come out to see at rallies in the middle of a pandemic. But it was not clear that he had changed the tenor of the campaign, or made any sort of appeal to voters who are still persuadable.

Mr. Biden also didn’t appear overly rattled, and took opportunities to point out that the country has become “weaker, sicker” and “more divided” under Mr. Trump’s leadership.

“Will you shut up, man?” Mr. Biden said at one point, channeling, perhaps, the voice of a tired nation that has been tuned into the Trump show daily for four years. At another point, Mr. Biden called his opponent racist and “Putin’s puppy.”

But he managed to look interested in issues, rather than a slapfest. “I’d like to talk about climate change,” the moderator, Chris Wallace, said, cutting off a discussion about Hunter Biden.

“So would I,” Mr. Biden said.

Asked what he believed about “the science of climate change,” President Trump responded with a litany of platitudes and misinformation.

Mr. Trump said he wanted “crystal clean water and air,” “beautiful, clean air” and “immaculate air, immaculate water,” even though his administration has reversed Obama-era regulations on air and water pollution.

He went on to claim that the United States has “the lowest carbon” (it doesn’t), that “people are actually very happy about what’s going on” (a large majority of Americans oppose Mr. Trump’s climate policies), and that California would not be burning “if you had forest management” (this is misleading; while forest management can contribute to fire prevention, many of the wildfires raging in California and elsewhere on the West Coast are not forest fires at all, and the science is very clear that climate change is making them worse).

Joseph R. Biden Jr., in response, outlined several elements of his climate plan, including making federal investments in renewable energy, weatherizing four million buildings, and pressuring Brazilian officials to stop deforestation in the Amazon.

Mr. Trump has repeatedly denied the scientific facts of climate change, and his administration has weakened or eliminated numerous environmental regulations. That record has become more difficult for him to defend as the sorts of disasters amplified by climate change become more frequent and more intense.

Joseph R. Biden Jr. tried to resurrect a potent line of attack against President Trump, referring to a report this month that he had privately referred to American soldiers killed in combat as “losers” and “suckers.”

But the moment led to perhaps the most bitter and emotional exchange of the night, involving references to Mr. Biden’s two sons, Hunter and Beau Biden.

“Speaking of my son, the way you talk about the military — the way you talk about them being losers and being, and just being suckers — my son was in Iraq and he spent a year there,” Mr. Biden said, referring to his son Beau, who served in the Iraq war and died in 2015 of brain cancer. “He got the Bronze Star. He got the Conspicuous Service Medal. He was not a loser. He was a patriot. And the people left behind there were heroes.”

“Are you talking about Hunter?” Mr. Trump interjected.

“I’m talking about my son Beau Biden,” Mr. Biden replied.

“I don’t know Beau, I know Hunter,” Mr. Trump said. “Hunter got thrown out of the military. He was thrown out, dishonorably discharged for cocaine use. And he didn’t have a job until you became vice president.”

“That’s not true,” Mr. Biden said. “None of that is true.”

Mr. Trump then accused Hunter Biden of making “a fortune in Ukraine and China.”

“My son. My son,” Mr. Biden said, visibly shaken. “My son, like a lot of people, like a lot of people we know at home, had a drug problem. He’s overtaken it. He’s fixed it. He’s worked on it. And I’m proud of him.”

Allies of Mr. Biden had braced for ugly personal attacks from Mr. Trump on the debate stage, aware that Mr. Biden has a temper and is deeply protective of his family. While Mr. Biden did not lose his temper, the exchange was perhaps the most wrenching of the night, as a sitting president seemed to dismiss Mr. Biden’s deceased son and accuse his living son of being a drug addict.

Joseph R. Biden Jr. and President Trump tussled over an issue that has roiled the country in recent months: racism.

“Why should voters trust you rather than your opponent to deal with the race issues facing this country over the next four years?” Chris Wallace, the moderator, asked both men.

It was an issue that played straight into the hands of Mr. Biden, who enjoys a significant lead over Mr. Trump among Black voters: A recent poll from The New York Times and Siena College showed that Mr. Biden led Mr. Trump among Black voters, 81 percent to 7 percent. And the Democratic Party is the political home for most Black Americans.

Mr. Biden tried to press his advantage, citing the white supremacist rally in Charlottesville, Va., in 2017, after which Mr. Trump said there had been “very fine people on both sides.”

“This man is a savior of African-Americans?” Mr. Biden asked, with mock incredulity.

Mr. Trump, for his part, immediately cited the 1994 crime bill, which created a range of new federal offenses and expanded the use of the death penalty, and was a point of vulnerability for the longtime Delaware senator throughout the primaries.

“They saw what you did,” Mr. Trump said.

Mr. Trump has tried to chip away at Mr. Biden’s support among Black people, hoping that even a few percentage points could tip the election. At the Republican National Convention last month, Mr. Trump’s party stretched hard to find African-Americans who would testify that the president was not a racist, in what represented an extraordinary effort to recast his record on issues of race.

Mr. Trump and Republicans have also seized on remarks Mr. Biden made in May, when he told a radio host that Black voters torn between voting for him and Mr. Trump “ain’t Black.” The comment, which Mr. Biden has apologized for, set off a firestorm online among liberal activists and conservatives alike. His words also threatened to reopen wounds from 2016, when many leaders felt Democrats had taken Black voters for granted.

Mr. Biden at the time swiftly tried to remedy his remarks.

“No one, no one, should have to vote for any party based on their race, their religion, their background,” he said. “There are African-Americans who think that Trump was worth voting for. I don’t think so, I’m prepared to put my record against his. That was the bottom line and it was, it was really unfortunate.”

A brief exchange between President Trump and Joseph R. Biden Jr. on coronavirus lockdowns highlighted some of the most fundamental differences in their approaches to the pandemic.

Asked about the prospects for economic recovery after the crash caused by the virus crisis, Mr. Biden spoke in detail — or at least as much detail as is possible in two minutes — about the reasons it has been difficult for schools and small businesses to reopen. It is expensive to reopen schools, he noted, and the Trump administration has not provided masks for teachers and students.

“He is insisting that we go forward and open when you have almost half the states in America with a significant increase in Covid deaths and Covid cases,” Mr. Biden said. “You can’t fix the economy until you fix the Covid crisis.”

Mr. Trump deflected blame for the virus, referring to it as the “China plague”; claimed that Democrats were opposed to reopening cities quickly for political reasons; and boasted: “I’m the one that brought back football. I brought back Big Ten football.” He did not describe measures that would make it easier to reopen the economy, but rather asserted broadly that it should have been done already.

Even as coronavirus cases spike once more, Mr. Trump has insisted that states can reopen, children can go to school, worshipers can go to church and he can hold rallies — but he has simultaneously sought to delegitimize the very measures, like consistent wearing of face masks, that experts say are most likely to make those activities safe.

Despite his best efforts to talk up his administration’s response to the virus crisis — and his efforts to change the subject — Mr. Trump has not been able to convince voters that his response was adequate, according to polls. A recent ABC News poll showed that 58 percent of voters disapproved of the president’s performance on the pandemic.

 

Joseph R. Biden Jr. was given an opportunity to lay out how President Trump has botched the country’s response to the coronavirus crisis, the key topic for the Democratic nominee and the subject where the president is most vulnerable.

“He said, ‘It is what it is,’” Mr. Biden said, referring to the president’s reaction to the grim milestone earlier this year that 100,000 people in the United States had been killed by the virus (the death toll is now over 200,000). “It is what it is, because you are who you are,” Mr. Biden said.

“We should be providing all the protective gear possible,” Mr. Biden said. “We should be providing the money the House has passed in order to be able to go out and get people the help they need to keep their businesses open.”

He added, “You should get out of your bunker and get out of the sand trap and your golf course and go in the Oval Office and bring together the Democrats and Republicans and fund what needs to be done now to save lives.”

Mr. Biden said voters should not trust the president on his promises of a vaccine within weeks. “He puts pressure and disagrees with his own scientists,” Mr. Biden said. He challenged voters that it was hard to believe him “in light of all the lies he’s told you about the whole issue relating to Covid.”

Mr. Trump defended his administration’s response, claiming that many Democratic governors had said he did a phenomenal job. Some Democratic governors over the spring walked a careful line because they did not want to risk alienating Mr. Trump and jeopardizing their ability to received desperately needed federal resources. But many Democratic governors criticized him. Gov. J.B. Pritzker of Illinois, for instance, said the federal government had “not lived up to its expectations” when it came to making coronavirus tests available.

“We got the gowns, we got the masks, we made the ventilators,” Mr. Trump said, claiming Mr. Biden would have failed to do so.

Mr. Trump said that his comment suggesting that ingesting disinfectant could help combat the virus was “said sarcastically, you know that.”

No issue has threatened Mr. Trump’s re-election more than a health crisis he has been unable to talk his way out of — one that has hurt him with older adults who are anxious for their lives, and complicated his attempts to appeal to more Black voters, who have been disproportionately affected by the virus.

The president, frustrated that the economic gains he had claimed credit for and had expected to help him win re-election were wiped away, has deliberately tried to play down the seriousness of the virus, hoping it would simply disappear. In January, Mr. Trump dismissed it as “one person coming in from China,” even though he knew it was far more deadly than the common flu he compared it to in public. He has also claimed falsely that the United States had “among the lowest case fatality rates of any major country anywhere in the world,” even though it ranks in the top third.

Even as coronavirus cases spike across parts of the country, Mr. Trump has insisted that states could reopen, children should go to school, people should be allowed to worship at church and that he should be able to hold campaign rallies. He has helped make the wearing of face masks, which his own experts say are the most important measure to stop the spread and keep Americans safe, the latest front of the culture war, rather than a measure embraced by all.

Despite his best efforts to talk up his administration’s response to the virus crisis — and his efforts to change the subject, completely — Mr. Trump has not been able to convince voters that his response was adequate, according to polls. A recent ABC News poll showed that 58 percent of voters disapproved of the president’s performance on the pandemic.

President Trump and Joseph R. Biden Jr. both invoked China during Tuesday’s presidential debate, as they argued over the coronavirus pandemic, climate change and the U.S. economy.

Mr. Trump deflected blame for the outbreak in the United States, calling the virus the “China plague” and casting doubt on whether the official Covid-19 death tolls in China and elsewhere were accurate. Mr. Trump also said that without the travel measures that he had imposed on China, millions of Americans would have died.

“It’s China’s fault,” he said of the crisis. “It should have never happened.”

Those measures, however, did not ban all travel from China. Nearly 40,000 people came to the United States from China from the end of January to April, after Mr. Trump’s restrictions were imposed. During the first half of January, when Chinese officials were underplaying the severity of the outbreak, no travelers from China were screened in the United States for potential exposure to the virus.

On Tuesday, Mr. Biden accused the president of taking the word of China’s leader, Xi Jinping, early in the crisis rather than insisting that American experts be allowed to conduct research in Wuhan, China, where the virus first emerged.

The president “told us what a great job Xi was doing,” Mr. Biden said.

Mr. Biden also brought up China as he criticized the president’s handling of the economy, saying that the United States has a higher deficit with China now than it did before Mr. Trump’s administration took power. But that deficit — the gap between what the United States exports to China and what it imports — fell sharply between 2018 and 2019 as Mr. Trump’s trade war suppressed commerce between the world’s largest economies.

Mr. Trump focused on China in one of several attacks on Mr. Biden’s son Hunter Biden. The younger Mr. Biden previously sat on the board of an investment fund with links to the Chinese government.

“China ate your lunch, Joe,” he said. “And no wonder, your son goes in and he takes out, he takes out billions of dollars. He takes out billions of dollars to manage. He makes millions of dollars.”

A lawyer for Hunter Biden has said that he resigned from the board in April and was never paid for his role.

Chinese officials did not publicly comment on the debate. But Hu Xijin, the editor of the Global Times, a Communist Party-run newspaper, said on Twitter that Mr. Trump and Mr. Biden “obviously did not show an exemplary role to American people on how to engage in debates.”

“Such a chaos at the top of U.S. politics reflects division, anxiety of U.S. society and the accelerating loss of advantages of the U.S. political system,” added Mr. Hu, a combative supporter of President Xi.

Others weighed in on Chinese social media platforms, saying that the debate had left them puzzled and amused.

One user said that Mr. Trump’s frequent interruptions of Mr. Biden lent a “comedic feel” to what should have been a serious discussion, while another compared the debate to a quarrel at a vegetable market.

Coral Yang contributed research.

Pressed by the moderator, Chris Wallace, about how much he paid in federal income taxes in 2016 and 2017, President Trump falsely said he paid “millions of dollars” in each year — and promised “you’ll get to see it.”

Of course, Mr. Trump, the only recent presidential candidate who has declined to publicly release his tax returns, paid $750 in federal income taxes in 2016 and 2017 — and has leveraged his enormous losses as a businessman to garner questionable tax breaks and refunds, a major New York Times investigation published on Sunday found.

Mr. Trump, dating to his 2016 presidential campaign, has repeatedly pledged to release his tax returns and never has done so. During Tuesday’s debate he argued that tax avoidance schemes he utilized reveal his intelligence and were a product of tax laws written by the Obama administration.

“Chris, let me tell you something, I don’t want to pay tax,” Mr. Trump said. “Like every other private business person, unless they’re stupid, they go through the laws.”

“Show us your tax returns,” Joseph R. Biden Jr. interjected at one point.

“You’ll see it as soon as it’s finished,” said Mr. Trump, who has repeatedly made that promise — without disclosing his returns — since he entered the presidential campaign in 2015.

Mr. Biden was one of the least wealthy officials in the Obama administration, and even so, paid about $91,000 in federal income taxes during 2016, the last year he was a government employee, with family income of around $400,000. In 2018, he earned about 10 times as much, and paid $1.5 million to the federal government.

Mr. Trump paid no income taxes at all in 10 of the previous 15 years — largely because he reported losing much more money than he made. He owes more than $400 million in debt due over the next several years and is still mired in a decade-long audit dispute with the Internal Revenue Service over the legitimacy of a $72.9 million tax refund that he claimed.

As a private citizen, Mr. Trump has long sought to shield from the public the true nature of his finances, and made claims about his wealth that were either impossible to verify or later found to be gross overestimates.

As president, he has used the levers of government to avoid any disclosure of his financial affairs; Mr. Trump’s Treasury secretary, Steven Mnuchin, has repeatedly shielded him from congressional scrutiny.

Mr. Biden pledged to eliminate the 2017 tax law Mr. Trump signed that delivered steep tax cuts for corporations and the wealthy.

“He says he’s smart because he can take advantage of the tax code,” Mr. Biden said. “I’m going to eliminate the Trump taxes and we’re going to invest in the people who need help.”

Mr. Trump once again sought to interrupt Mr. Biden.

Mr. Biden responded: “You’re the worst president America has ever had.”

Former Vice President Joseph R. Biden Jr. has made one thing clear in Tuesday’s presidential debate: Don’t trust President Trump.

While Mr. Trump repeatedly spoke over Mr. Biden and over the moderator, Chris Wallace, Mr. Biden spoke directly to the camera, addressing viewers watching at home and sharing what public polling shows is a large distrust of the president.

On the search for a coronavirus vaccine, Mr. Biden, speaking directly to the camera, said: “We’re for a vaccine, but I don’t trust him at all, nor do you, I know you don’t. You trust scientists.”

Mr. Biden also reminded the audience that Mr. Trump had repeatedly prognosticated that the coronavirus would disappear on its own.

“This is the same man that told you by Easter this would be gone away,” Mr. Biden said. “By the warm weather it would be gone, like a miracle. And maybe you could inject bleach in your arm, and that would take care of it.”

Mr. Trump interjected, arguing that his infamous bleach remark had been “sarcastic.”

The debate turned to the topic of how President Trump and Joseph R. Biden Jr. are campaigning during the pandemic, as the two men continue to take starkly different approaches to holding events during the coronavirus pandemic.

Mr. Trump has resumed large, crowded rallies, sometimes indoors, while Mr. Biden continues to hold small, socially distanced events that adhere to public health guidelines.

Mr. Trump suggested Mr. Biden’s approach was because “nobody will show up.” By contrast, the president boasted, “We have tremendous crowds.”

The president also claimed that “We’ve had no negative effect” from holding rallies. But that is not necessarily true. A surge in coronavirus cases in and around Tulsa, Okla., after Mr. Trump held a rally there in June, for instance, was probably connected to Mr. Trump’s rally, the city’s top health official said in early July. Herman Cain, the chief executive of a pizza chain and a former presidential candidate, tested positive for the coronavirus shortly after attending Mr. Trump’s Tulsa rally and later died from Covid-19, though it was not clear where he had contracted the virus.

Mr. Biden’s guarded strategy reflects his campaign’s gamble that voters will reward a sober, responsible approach to the coronavirus crisis that mirrors the way it has upended their own lives.

Fact-Checking Trump on His Campaign Rallies

At least eight staff members who helped plan President Trump’s indoor rally in June in Tulsa, Okla., tested positive for the coronavirus.

Sept. 29, 2020

President Trump, who has left a wreckage of presidential norms in his path, can add another: televised debates — turning a once-civil forum governed by strictly enforced rules into an ugly free-for-all by refusing to allow his opponent, or the moderator, to finish a sentence uninterrupted.

Mr. Trump has one political gear — disruption — and on Tuesday he lambasted his Democratic opponent, Joseph R. Biden Jr., and the debate moderator, Chris Wallace, in an attempt to draw both into a brawl, both to divert attention from his shortcomings and to deny Mr. Biden the opportunity to appear presidential.

The president — an incumbent who runs with the alacrity of a challenger — repeatedly interrupted Mr. Biden. At times, he appeared less like a participant than a heckler, diverting and interrupting both Mr. Wallace and Mr. Biden from asking and answering questions — and accusing both of being in cahoots.

In an extraordinary moment, Mr. Wallace, the host of “Fox News Sunday,” raised his voice to stop the president from shouting over Mr. Biden.

“Mr. President. Your campaign agreed both sides get two-minute answers. Uninterrupted. Your side agreed. Observe what your campaign agreed to,” Mr. Wallace said — which silenced the president for less than a minute.

The clamor began when Mr. Biden criticized Mr. Trump’s efforts to dismantle the Affordable Care Act, a key vulnerability, especially in the wake of the coronavirus pandemic.

“Here’s the deal, the fact is that everything he’s saying so far is simply a lie. I’m not here to call out his lies, everybody knows he’s a liar,” Mr. Biden said.

“You graduated last in your class, not first in your class,” Mr. Trump interjected.

“Mr. President, can you let him finish, sir,” said Mr. Wallace, who cautioned Mr. Trump several times during a 90-minute scrum that the NBC anchor Lester Holt later called “a low point in political discourse.”

Yet Mr. Trump — determined to go on the attack to prove Mr. Biden was too weak to succeed him — kept interrupting him without respect to the agreed-upon subject format.

At one point he interrupted Mr. Biden’s attempt to talk about his son Beau, a decorated veteran who died of a brain tumor in 2015, in the context of disparaging remarks Mr. Trump has reportedly made about the military.

“My son was in Iraq and spent a year there. He got the Bronze Star. He got the Conspicuous Service medal. He was not a loser. He was a patriot,” Mr. Biden said.

“Talking about Hunter?” Mr. Trump said, referring to Mr. Biden’s younger son Hunter, who took a high-paying seat on the board of Ukrainian gas company when his father was in office.

“Will he just shush for a minute,” said Mr. Biden, who was successful — at the start of the debate, at least — in not letting the president get under his skin.

Then, after being swept away on a torrent of Trump talk, Mr. Biden said, “Folks, do you have any idea what this clown’s doing?”

 

It didn’t take 15 minutes for President Trump to try to verbally steamroll both Chris Wallace, the debate moderator, and Joseph R. Biden Jr.

Mr. Trump repeatedly spoke over Mr. Wallace as he tried valiantly to ask why Mr. Trump hadn’t produced the health care plan he promised, then continued to interrupt Mr. Biden as he sought to answer questions.

Mr. Trump’s tactics serve to make him the story of the debate — a character trait that has run throughout his tenure as president and, during the past six months, the general election of the presidential campaign.

Even when Mr. Biden faced questions from Mr. Wallace that would have put him on the defensive, Mr. Trump couldn’t resist jumping in to offer his own commentary to slam Mr. Biden.

“He doesn’t want to answer the question,” Mr. Trump shouted as Mr. Biden sought to respond to a question about whether he would add justices to the Supreme Court.

Mr. Biden shot back: “Would you shut up, man?”

Almost as soon as the debate began, the topic shifted to health care — signaling just how pivotal both parties feel the issue is in the presidential election.

Joseph R. Biden Jr., the Democratic nominee, followed the strategy he has been telegraphing since the death of Justice Ruth Bader Ginsburg, using the opening issue — the Supreme Court — to talk about health care. Addressing the stakes of the Supreme Court battle, Mr. Biden said President Trump wanted to dismantle the Affordable Care Act, a point he has hit repeatedly in the past week.

“What’s at stake here is the president has made it clear he wants to get rid of the Affordable Care Act,” Mr. Biden said.

“Your party wants to go socialist medicine,” Mr. Trump shot back, an apparent reference to the “Medicare for all” style health care plan supported by some Democrats, including Senator Bernie Sanders of Vermont.

Mr. Biden swiftly rebutted Mr. Trump’s characterization. “The party is me,” he said. “Right now, I am the Democratic Party.”

Mr. Biden and his advisers have tried to bring the conversation back to health care at nearly every turn, mindful that the strategy worked for the Democratic Party in the 2018 midterm elections.

Unlike some of his Democratic rivals, Mr. Biden does not support Medicare for all, a government-run health insurance system under which private insurance would be eliminated.

Instead, he wants to expand the Affordable Care Act — the health care law that was enacted when he was vice president — by offering a public option that would allow anyone to sign up for a government-run health plan.

His proposal would also lower the maximum percentage of income people could spend on premiums and enable more people to get subsidies to help pay for their health insurance.

President Trump on Tuesday mounted a simple defense of his right to confirm a replacement for Justice Ruth Bader Ginsburg before the Nov. 3 vote: “Elections have consequences,” he said.

“I will tell you very simply, we won the election,” Mr. Trump said at the first general election debate. “Elections have consequences. We have the Senate.”

In other words, he will do it because he can.

In the past, he has not addressed the hypocrisy on the part of Republicans, who refused to even consider President Barack Obama’s nominee after Justice Antonin Scalia died in February 2016, citing the coming election.

Mr. Trump claimed Tuesday night that Democrats would do what he is doing, if they had been able to do so.

“They had Merrick Garland but the problem is, they didn’t have the election, and they were stopped,” he said.

Mr. Biden, in his first comments on Tuesday about Judge Amy Coney Barrett’s nomination, argued that Mr. Trump was simply trying to push through his nominee because “what’s at stake here is the president has made it clear he wants to get rid of the Affordable Care Act.”

Mr. Biden said Judge Barrett seemed like a “very fine person,” being careful to avoid any criticisms of her Catholic faith that might give Republicans a new line of attack. But he said it wasn’t right to push it through before the election.

“The election has already started,” he said. “Tens of thousands of people have already voted. The thing that should happen is, we should wait. We should wait and see what the outcome of this election is.”

President Trump and former Vice President Joseph R. Biden Jr. have begun the first general election debate of the 2020 campaign.

Mr. Trump and Mr. Biden did not shake hands as they stepped to their lecterns, a nod to coronavirus restrictions, according to Chris Wallace of Fox News, the debate moderator. The debate is planned for 90 minutes with no commercial breaks.

“How you doing, man,” Mr. Biden said, as he extended his arms in an air hug to Mr. Trump.

Television cameras showed the first lady, Melania Trump, Dr. Jill Biden and the extended Biden and Trump families entering the debate hall at Case Western Reserve University in Cleveland.

Mr. Wallace reminded the audience that the Cleveland Clinic has designed health and safety precautions for the debate and welcomed the candidates to the stage. Then he began the debate with the first subject: The Supreme Court.