The events showcased striking differences in temperament, views on racial justice and approaches to the pandemic that has reshaped the nation.
Mr Trump was defensive about his government’s handling of the coronavirus, which has claimed more than 215,000 American lives, and evasive when pressed about whether he took a required Covid-19 test before his first debate with Mr Biden.
Angry and combative, he refused to denounce the QAnon conspiracy group — and only testily did so on white supremacists.
We have to heal this nation. pic.twitter.com/wD45ZGcKO2
— Joe Biden (@JoeBiden) October 16, 2020
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The president also appeared to acknowledge he was in debt and left open the possibility that some of it was owed to a foreign bank.
He insisted that he did not owe any money to Russia or any “sinister people” and suggested that being $400 million (£312 million) in debt was a “very very small percentage” compared to his overall assets.
Meanwhile Mr Biden, appearing nearly 1,200 miles away, denounced the White House’s handling of the virus, declaring that it was at fault for closing a pandemic response office established under former president Barack Obama.
Though vague at times, he acknowledged it was a mistake to support a 1994 crime bill that led to increased black incarceration and suggested he finally will offer clarity on his position on expanding the Supreme Court if Mr Trump’s nominee to the bench is seated before election day.
The president, less than two weeks after being diagnosed with Covid-19, dodged directly answering whether he took a test the day of the September 29 debate, only saying “possibly I did, possibly I didn’t”.
Debate rules required that each candidate, using the honour system, had tested negative prior to the Cleveland event, but Mr Trump spoke in circles when asked when he last tested negative.
It was his positive test two days later that created Thursday’s odd spectacle, which deprived most viewers of a simultaneous look at the candidates just 19 days before the election.
The presidential rivals took questions in different cities on different networks: Mr Trump on NBC from Miami, Mr Biden on ABC from Philadelphia.
Mr Trump backed out of plans for the presidential face-off originally scheduled for the evening after debate organisers said it would be held virtually following his Covid-19 diagnosis.
The difference in the men’s tone was immediate and striking.
The president was loud and argumentative, fighting with the host, Savannah Guthrie, complaining about the questioning — and eventually saying for the first time that he would honour the results of a fair election, but only after casting an extraordinary amount of doubt on the likeliness of fairness.
If I'm elected president, you won't hear me race-baiting, you won't hear me dividing — you'll hear me trying to unify. pic.twitter.com/PNsBW8OQmX
— Joe Biden (@JoeBiden) October 16, 2020
“And then they talk ‘Will you accept a peaceful transfer,'” Mr Trump said.
“And the answer is, ‘Yes, I will.’ But I want it to be an honest election, and so does everybody else.”
He again sought to minimise revelations from a New York Times investigation that he has more than $400 million (£312 million) in debt and suggested that reports are wrong that he paid little or no federal income taxes in most years over the past two decades.
He insisted that Americans should not be alarmed by his debt and repeatedly insisted that he is “under-leveraged”.
“It’s a tiny percentage of my net worth,” Mr Trump said of his reported debt.
But he left open the possibility that some of his debt is owed to a foreign bank by saying: “No, I don’t owe Russia money. I owe a very, very small, it’s called mortgages.”
Mr Biden took a far different, softer, approach with audience questions.
The former vice president, who struggled growing up with a stutter, stuttered slightly at the start of the program and at one point squeezed his eyes shut and slowed down his response to clearly enunciate his words. At times his answers droned on.
The Democratic nominee also brought a small card of notes on stage and referred to it while promising to roll back tax cuts for the wealthiest Americans.
Mr Biden vowed to say before election day whether he will support expanding the number of justices on the Supreme Court if Democrats win the presidency, the Senate and hold the House after November.
He has for weeks refused to answer the question but went further on Thursday night.
He said he was “still not a fan” of expanding the court, but that his ultimate decision depended on how the confirmation of Amy Coney Barrett to the Supreme Court “is handled” and “how much they rush this”.
The words of a president matter. pic.twitter.com/ABrbg5xTkg
— Joe Biden (@JoeBiden) October 16, 2020
Mr Biden also blasted the president’s foreign policy, declaring that “’America first’ has made ‘America alone’” and “this president embraces all the thugs in the world”.
He turned introspective when asked what it would say if he lost.
“It could say that I’m a lousy candidate, that I didn’t do a good job,” Mr Biden said.
“But I think, I hope that it doesn’t say that we’re as racially, ethnically and religiously at odds as it appears the president wants us to be.”
Mr Biden said he plans to participate in next week’s debate but that he would ask the president to take a Covid-19 test before arriving.
The two men are still scheduled to occupy the same space for a debate for a second and final time next week in Nashville.
