President Biden rejected concerns about his fumbling performance in the first presidential debate last month in a prime-time interview on Friday.

In the interview with George Stephanopoulos of ABC News, Mr. Biden downplayed and misstated polls showing him falling farther behind former President Donald J. Trump since the debate, exaggerated Mr. Trump’s proposals and made hyperbolic statements about his own record and recent events.

Here’s a fact check.

what Was SAID

“After that debate, I did 10 major events in a row, including until 2 o’clock in the morning after the debate. I did events in North Carolina. I did events in — in — in Georgia, did events like this today, large crowds, overwhelming response, no — no — no slipping.”

This is exaggerated. Since the debate on June 27, Mr. Biden has traveled up and down the East Coast and participated in more than a dozen events, according to his public calendar. Whether or not the events can be considered “major” and crowds “large” are matters of opinion, but Mr. Biden did misspeak at several.

Before the interview on Friday, Mr. Biden said of Mr. Trump at a rally in Wisconsin that he would “beat him again in 2020.”

At a Fourth of July barbecue with military members and their families, Mr. Biden referred to Mr. Trump as “one of our former colleagues” before correcting himself.

And at a fund-raising reception in East Hampton, New York, he confused Italy and France when referring to the location of a veterans’ cemetery he recently visited.

What Was Said

“I’m the guy that shut Putin down. No one thought could happen.”

This needs context. Mr. Biden’s campaign said he was referring to reports that Russian President Vladimir V. Putin had hoped for and failed to achieve a quick and decisive victory in Ukraine and that Russia’s military had suffered heavy losses. That, the campaign said, was possible in part because of Mr. Biden’s marshaling of allies and aid.

Still, Mr. Putin’s war in Ukraine continues two years later. And despite heavy sanctions imposed by the United States and other Western countries, its economy continues to grow. The World Bank recently upgraded Russia from a upper-middle-income country to a high-income one.

What Was Said

“All the pollsters I talk to tell me it’s a tossup. It’s a tossup. And when I’m behind, there’s only one poll I’m really far behind, CBS poll and NBC, I mean, excuse me.”

This is exaggerated. The Biden campaign pointed a poll from Bloomberg showing Mr. Trump leading by two percentage points, and argued that most polls showed Mr. Trump’s lead was within the margin of error — a statistical indication of uncertainty in polling results.

Although it is true that many of the polls had Mr. Trump’s lead within the margin of error, he is ahead in most public polling. FiveThirtyEight’s average of national polls showed Mr. Trump ahead by 2.5 percentage points while Real Clear Politics’ average showed Mr. Trump leading by 3.3 percentage points as of Friday night.

Out of 12 polls aggregated by Real Clear Politics and 14 by FiveThirtyEight, only one, from Reuters/Ipsos, showed a tie. The Biden campaign said Mr. Biden had misspoken and meant The New York Times/Siena College poll, which had a six-point lead for Mr. Trump. Polls by The Wall Street Journal and CNN showed a similar advantage for Mr. Trump.

What Was Said

“The New York Times had me behind before anything having to do with this race — had me hind — behind 10 points. Ten points they had me behind. Nothing’s changed substantially since the debate in The New York Times poll.”

This is misleading. The New York Times/Siena College poll showed Mr. Trump’s lead had grown by three points among both likely and registered voters. Mr. Biden also exaggerated The Times’ pre-debate polling results.

Before the debate, Mr. Trump led among likely voters by 48 percent to 44 percent (a three-point margin before rounding) and among registered voters by 48 percent to 42 percent in the Times poll from June. Following the debate, Mr. Trump led 49 percent to 43 percent, and 49 to 41 percent among registered voters (a nine-point margin before rounding).

The Biden campaign argued that the poll’s margin of error was 2.8 percent so Mr. Trump’s lead was within that margin, suggesting a minor shift.

What Was Said

“This is a guy who told us to put bleach in our arms to deal with Covid, with a million — over a million people died. This is a guy who talks about wanting to get rid of the health care provision we put in place. This is a guy who wants to give the power back to Big Pharma to be able to charge exorbitant prices for drugs.”

This is exaggerated. Mr. Trump’s comments, in April 2020, about the efficacy of disinfectants and light as treatments for the coronavirus sparked uproar and confusion. He did not instruct people to inject bleach, but suggested that doing so with a disinfectant was an “interesting” concept to test out.

At an April 2020 news conference, a member of Mr. Trump’s coronavirus task force said that the virus dies under direct sunlight and that applying bleach in indoor spaces kills the virus in five minutes and isopropyl alcohol in 30 seconds.

Mr. Trump responded: “And then I see the disinfectant, where it knocks it out in a minute. One minute. And is there a way we can do something like that, by injection inside or almost a cleaning? Because you see it gets in the lungs, and it does a tremendous number on the lungs. So it would be interesting to check that.”

The Biden campaign said that Mr. Biden’s comment about health care was referring to Mr. Trump’s recent proposals to repeal and replace the Affordable Care Act. While he campaigned on that proposal in 2016, his current position is vague and he has not yet released a health care plan.

Though Mr. Trump continues to criticize the health care law as an expensive “disaster,” he said in a January rally in Iowa that his administration would “be either working on Obamacare or doing something new.” Mr. Trump also wrote on social media in March that “I’m not running to terminate the ACA,” though he has not released any details on what he would do.

Similarly, Mr. Trump has not said anything about terminating a provision in the Inflation Reduction Act, the climate change, health and tax law, allowing Medicare to negotiate drug prices. While some Republican lawmakers have expressed interest in repealing that provision, Mr. Trump has not commented.

What Was Said

“Well, Mark is a good man. We’ve never had — he also tried to get the nomination too.”

This is misleading. Asked about reports that Senator Mark Warner of Virginia was working to convene fellow Senate Democrats to discuss Mr. Biden’s future as the party’s presidential nominee, Mr. Biden dismissed those reports by claiming that Mr. Warner was a former political rival.

But Mr. Warner has never run for president. Mr. Warner had explored a bid nearly two decades ago, but in 2006 announced that he would not seek the nomination. Mr. Biden briefly ran for president in 2008, but quit the race in January after poor results in the Iowa caucuses.

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