rump refued to disavow a bizarre online conspiracy, while Mr Biden, a Democrat, would not divulge plans for the Supreme Court.
Both candidates were on the defensive at times on their records, Mr Trump for a range of issues and Mr Biden on race.
Opinion polls indicate Mr Biden has a solid lead over Mr Trump.
However, polling is still very close in several key states which could decide the election.
More than 18 million people have already voted in person or by post for the 3 November vote.
Thursday night's town halls, as TV voter question-and-answer events are known in the US, replaced a cancelled second presidential debate. Mr Trump had refused to join that showdown virtually, following the recent Covid-19 diagnosis from which he now appears fully recovered.
Fact-checking Trump and Biden town hall events Who is ahead - Trump or Biden? A really simple guide to the US election What were the key moments for Trump? During his primetime event hosted by TV network NBC in Miami, Florida, the president was asked about the QAnon conspiracy theory, whose adherents believe that Mr Trump is battling a clandestine network of elites, often involving Satanic plots and child trafficking.
When moderator Savannah Guthrie asked Mr Trump whether he would reject them, he replied: "I know nothing about QAnon."
Ms Guthrie said she had just told him about the group, which has been labelled a potential terrorist threat by the FBI.
The president said: "I know nothing about it, I do know they are very much against paedophilia, they fight it very hard."
Mr Trump instead turned his fire on antifa, a loose-knit movement of mainly far-left activists blamed by the US Department of Justice for civil disorder in American cities during racial justice protests over the last few months.
YouTube cracks down on QAnon conspiracy theory What is QAnon? For the first time, the president said he would accept a peaceful transfer of power if he lost next month's election, even as he expressed fears for the integrity of the vote. Federal election officials say there has been no evidence of widespread ballot fraud.
"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."
Mr Trump deflected other questions about healthcare and tax returns and whether he took a coronavirus test on the day of his last debate with Mr Biden, saying: "Possibly I did, possibly I didn't."
The president spent much of the town hall arguing with the moderator, who disputed many of his statements.
But he beamed when one female voter prefaced her question by saying: "You're so handsome when you smile!"