Both candidates took their place behind their lecterns on the debate stage in Atlanta just after 9 p.m. as the debate got underway. They did not shake hands. 

With no opening statements, moderators Jake Tapper and Dana Bash jumped right into questioning.

Mr. Biden was asked to respond to the economic pain Americans are feeling because of inflation, from the grocery store to the housing market. The president figuratively pointed his finger straight at Trump.

"We've got to take a look at what I was left with when I became president, what Mr. Trump left me," the president said, with a noticeably raspy voice. "We had an economy that was in freefall. The pandemic was so badly handled. … What we had to try to do was put things back together again, and that's exactly what we began to do." 

The president pointed to various moves his administration has made to lower prices for Americans, including curbing insulin costs to closer to $15 than $400. 

Trump insisted the U.S. "had the greatest economy in the history of our country" when he was president, and pointed the finger back at Mr. Biden. 

"Inflation is killing our country, it is absolutely killing us," Trump said. 

Trump's claim that during his presidency the U.S. had the "greatest economy in the history of the country" is false by many of the common metrics used to judge economic performance. The claim struggles when looking at GDP. Excluding the 2020 pandemic, growth after inflation under Trump averaged 2.67%, according to figures from the World Bank. This is far from the GDP growth under Democratic President Bill Clinton, of 4%, according to World Bank data. Including the time after COVID spread, that average drops to 1.45%. 

Trump claimed, falsely, that the only jobs Mr. Biden created were for "illegal immigrants," and "bounce back" jobs in the aftermath of the COVID-19 pandemic.

Trump also defended his proposal to impose a 10% tariff on all foreign products entering the U.S. 

"It's not going to drive them higher," Trump insisted, contradicting the view of many economic experts. "It's just going to cost countries that have been ripping us off for years like China and many others, in all fairness to China."

Trump took aim at the president's record during questioning about the two candidates' economic policies, saying "we've become like a third world nation" during Mr. Biden's time in office. Trump claimed that his own tax cuts "spurred the greatest economy that we've ever seen," touting his economic approach, along with his record on COVID-19.

"I gave him an unbelievable situation," Trump said of Mr. Biden, adding that the current president has done a "very poor job."

"Throughout the entire world we're no longer respected as a country," Trump said. "They don't respect our leadership, they don't respect the United States anymore."

Trump said he agreed with the Supreme Court's decision earlier this month preserving access to abortion pills, when the justices rejected a challenge targeting the availability of the widely used abortion pill mifepristone. Trump said he agreed with the decision and "will not block it."

"Fifty-one years ago you had Roe v. Wade and everybody wanted to get it back to the states, everybody," Trump said, touting his appointment of three justices to the court who voted to overturn the decision guaranteeing a right to an abortion in 2022.

The former president said that now, the states are "working it out." He noted that he believes there should be exceptions for rape, incest and for protecting the life of the mother, a stance he has repeated in recent months after announcing in April that abortion restrictions should be left up to states, rather than federal restrictions. 

Mr. Biden said Trump's contention that "everybody" opposed Roe v. Wade was "ridiculous."

"The fact is that the vast majority of constitutional scholars supported Roe when it was decided, supported Roe. And ... this idea that they were all against it is just ridiculous," he said.

Mr. Biden stumbled in the first minutes of the debate, struggling to name Medicare when he was answering a question about the tax rate for wealthy Americans. 

"We have 1,000 trillionaires in America — I mean billionaires in America. And what's happening? They're in a situation where they, in fact, pay 8.2% taxes, if they just paid 24%, 25% — either one of those numbers — we'd raise $500 million dollars — billion dollars, I should say — in a 10-year period," he said, listing off a number of priorities like paying for child care, health care and "making sure that we're able to make every single solitary person eligible for what I've been able to do with the COVID, excuse me, with, dealing with everything we have to do with, uh…" 

The president then paused and struggled to come up with the word. 

"Excuse me," he said, "dealing with everything we have to do with…" 

The president then paused again. 

"Look, if we finally beat Medicare," he continued. 

"Thank you, President Biden," Tapper said. "President Trump?" 

"He did beat Medicaid, he beat it to death," Trump said. 

Trump tore into Mr. Biden over migrants who have illegally crossed the border, including some migrants who have committed crimes.

"He decided to open up our border, open up our country to people that are from prisons, people that are from mental institutions, insane asylums, terrorists. We have the largest number of terrorists coming into our country right now, all terrorists, all over the world, not just in South America, they come from the Middle East, everywhere," Trump said. 

Trump insisted the U.S. had the "safest border in history" when he was president. 

"There's never been anything like it, and people are dying all over the place, including the people that are coming up in caravans," Trump said. 

Mr. Biden punched back.

"The only terrorist who has done anything crossing the border is one who came along and killed three — in his administration — an al Qaeda person in his administration — killed three American soldiers," Mr. Biden said. "Killed three American soldiers. That's the only terrorist that's — I'm not saying no terrorist ever got through, but the idea they're emptying their prisons, we're welcoming these people, that's simply not true, there is no data to support what he said. Once again, he's exaggerating, he's lying." 

Tapper asked Trump to respond to voters who are concerned about a repeat of the attack on the Capitol on Jan. 6, 2021.

"After you rallied your supporters that day, some of them stormed the Capitol to stop the constitutionally mandated counting of electoral votes," Tapper said. "As president, you swore an oath to 'preserve, protect and defend' the Constitution. What do you say to voters who believe that you violated that oath through your actions and inactions on January 6 and worry that you'll do it again?"

"Well, I don't think too many believe that, and let me tell you about Jan. 6," Trump said. "On Jan. 6, we had a great border. Nobody coming through, very few. On Jan. 6, we were energy independent. On Jan. 6, we had the lowest taxes ever. We had the lowest regulations ever. On Jan. 6, we were respected all over the world, all over the world we were respected. And then he comes in and we're now laughed at. We're like a bunch of stupid people."

Tapper pressed Trump to ask the question. 

"Well, I didn't say that to anybody, I said 'peacefully and patriotically,'" Trump responded, before blasting former House Speaker Nancy Pelosi.

The conversation turned to Trump's conviction last month in his New York "hush money" criminal trial. Mr. Biden took aim at the former president during questioning about the Jan. 6 attack on the Capitol, saying "the only person on this stage who's a convicted felon is the man I'm looking at right now."

But Trump quickly worked to deflect, pointing to Mr. Biden's son, Hunter, before suggesting that the president himself could become a convicted felon, as well. 

"When he talks about a convicted felon, his son is a convicted felon," Trump said. "He could be a convicted felon as soon as he gets out of office … Joe could be a convicted felon with all of the things he's done."

Trump is currently awaiting a Supreme Court ruling on his contention that presidents have "absolute immunity" for acts committed while in office.

Mr. Biden pointed to Trump's numerous charges across four criminal cases, while asking about how much the former president owes in civil cases.

"You have the morals of an alley cat," Mr. Biden said. 

Trump responded directly, saying, "I didn't have sex with a porn star."

Forty-five minutes into the debate, sources familiar with the president's debate prep confirmed that Mr. Biden has had a cold for the past few days. Hence the raspy voice.

One top official said Mr. Biden was examined by the White House doctor at Camp David, who confirmed he has a cold. The president tested negative for COVID, two of the sources said.

During one exchange, the two candidates abandoned responses to more substantive questions to descend into criticism of the other for being the worst president the country has ever seen. 

"He's the worst president," Trump said, during a response to a question about making child care more affordable. "He's the worst president in the history of our country." 

Mr. Biden staunchly rejected the claim, throwing it back on Trump and claiming that according to experts, Trump is the worst president in American history. 

"They said he was the worst in all presidential history," Mr. Biden said, citing a recent survey of political scientists. "That's a fact."

Given another opportunity to respond to the question on childcare, Trump pledged that "if I'm given another four years, I'll be the best."

The moderators asked Mr. Biden to address voters' concerns about his age. Currently 81, he would be 86 at the end of a second term. 

"Well, first of all, I spent half my career being criticized for being the youngest person in politics," Mr. Biden said, alluding to the fact that he was just 30 years old when sworn in as a senator in 1973. "I was the second-youngest person ever elected to the United States Senate, and now I'm the oldest. This guy's three years younger, and a lot less competent."

The president went straight back to his record on jobs, including 800,000 more in manufacturing. Mr. Biden also pointed his efforts on bringing jobs back to the U.S. 

"The idea that somehow we are this failing country, I've never heard a president talk like this before," Mr. Biden said. "We're the envy of the world." 

Trump, who would be 82 at the end of a second term, was also asked about voters' concerns over his age. 

"Well, I took two tests, cognitive tests, I aced them, both of them as you know, we made it public," Trump claimed. "He took none, I'd like to see him take one, just one, a real easy one. Like go through the first five questions, he couldn't do it."

"We knock on wood wherever we may have wood that I'm in very good health," Trump added, before turning to golf. "I just won two club championships, not even senior, two regular club championships. To do that, you have to be quite smart, and you have to be able to hit the ball a very long way." 

When the debate veered into the topic of whether Trump would accept the results of November's election, Trump said — after being asked a second time — that he would accept the results of the election "if it's a fair and legal and good election, absolutely."

"I will, absolutely, there's nothing I'd rather do," Trump said, adding that he would have "much rather" accepted the result of the 2020 election, but claimed that the "fraud and everything else was ridiculous." 

There was no widespread fraud that would have changed the outcome of the 2020 election.

The former president also said, when asked about political violence, that it's "totally unacceptable."

Mr. Biden called the former president a "whiner," saying of Trump's election denialism that "not one single court in America said any of your claims had any merit … but you continue to promote this lie." 

"I tell you what, I doubt you'll accept it because you're such a whiner," Mr. Biden said. "The idea if you lose again, you accepting anything, you can't stand the loss, something snapped in you when you lost the last time." 

House Democrats are concerned by Mr. Biden's debate performance. They had hoped the debate could propel Mr. Biden into the summer, but that didn't happen.

"I've never seen a freakout like this," one House Democrat familiar with conversations among lawmakers said Thursday night. The person cautioned that it's unclear how seriously some Democrats would push for Mr. Biden to step aside from the race. 

The president's former White House communications director, Kate Bedingfeld, expressed concern live on CNN, calling it a "really disappointing debate performance." 

"I don't think there's any other way to slice it," she said. "His biggest issue was to prove to the American people that he had the energy, the stamina — and he didn't do that."

— Ed O'Keefe and Kathryn Watson