“It’s hard to get a word in with this clown,” Biden said. “Excuse me, I mean, this president.”
Meanwhile Trump accused Biden of graduating “the lowest or almost the lowest in your class” when he attended university in the 1960s.
“Don’t ever use the word ‘smart’ with me,” Trump told his opponent. “Because you know what? There’s nothing smart about you, Joe.”
As well as Biden, Trump clashed with the debate moderator, telling Wallace: “First of all, I guess I’m debating you, not him. I’m not surprised.”
Wallace, to largely little effect, said: “The country would be better served if we allow both people to speak with fewer interruptions.”
The initial polls following the debate found most voters believed Biden put in the better performance. A poll of debate watchers by CBS News found that 48 per cent of debate watchers judged Biden to be the winner while 41 per cent said Trump. Sixty-nine per cent of respondents in that poll said the debate made them feel annoyed while 31 per cent said they were entertained.
A CNN poll of debate watchers found 60 per cent of respondents said Biden was the winner compared to 28 per cent for Trump, though that poll had a skew towards Democrats.
One of the more remarkable moments came when Trump refused to condemn white supremacists when asked to do so.
“Proud Boys, stand back and stand by,” Trump said, referring to a far-right group. “But I’ll tell you what, somebody’s got to do something about Antifa and the left.”
As expected, Trump attacked Biden’s son Hunter over his past consulting work for companies in China and Ukraine.
“China ate your lunch, Joe,” Trump said. “No wonder your son goes in and he takes out – billions of dollars. Takes out billions of dollars to manage. He makes millions of dollars.”
After defending his son, Biden said: “This is not about my family. It’s not about your family. It’s about the American people.”
Biden attacked Trump over allegations in The Atlantic that he described deceased military veterans as “suckers” and “losers”.
Referring to his late son Beau, who served in the military, Biden said: “He was not a loser, he was a patriot and the people left behind there are heroes.”
“I don’t know Beau, I know Hunter,” Trump responded, reverting to his attacks on Biden’s surviving son.
When Biden called Trump “totally irresponsible” for holding mass rallies without physical distancing requirements, Trump responded by mocking Mr. Biden’s more constrained events, telling the former vice president he would hold large events as well “if you could get the crowds”.
At several times throughout the debate Biden tried to address the American people directly, ignoring Trump’s interjections.
“You folks living in Scranton and Claymont and all the small towns and working-class towns in America, how are you doing?” Biden asked in a section on the economy.
Veteran political analyst Larry Sabato, of the University of Virginia, described the event on Twitter as “one of the least instructive presidential debates ever” and “a chaotic mess”.
He then called for the remaining two presidential debates to be cancelled.
Pulitzer prize-winning presidential historian Jon Meacham said Trump’s behaviour at the debate was “the lowest moment in the history of the presidency” since Andrew Johnson in the late 1800s.
Republican pollster Frank Luntz said: “This debate has actually convinced some undecided voters to not vote at all. I’ve never seen a debate cause this reaction.”
The Biden campaign announced they had raised $US3.8 million while the debate was on air, breaking their record for most money raised in a single hour.
Just hours before the debate Biden and his running mate Kamala Harris released their 2019 tax returns in an effort to highlight a recent series of New York Times reports alleging Trump has paid little to no tax over recent decades.
Biden’s returns showed that he and his wife Jill paid more than $US346,000 in federal taxes and other payments for 2019 on an income of nearly $US985,000 before seeking a refund of nearly $US47,000 they said they had overpaid the government.
“This is a historic level of transparency meant to give the American people faith once again that their leaders will look out for them and not their own bottom lines,” Biden’s deputy campaign manager, Kate Bedingfield, said on a call with reporters.
“Mr President, release your tax returns or shut up,” Bedingfield added.
Matthew Knott is North America correspondent for The Sydney Morning Herald and The Age.