The Republican Trump adopted a far more restrained tone than he did during their first presidential debate in September, which was quickly derailed by his constant interruptions and personal insults from both men.

The televised encounter in Nashville, Tennessee, on Thursday night represents one of the Republican Trump's last remaining opportunities to reshape a campaign dominated by a pandemic that has killed more than 221,000 people in the United States.

Opinion polls show Trump is trailing Biden, though the contest is tighter in some battleground states likely to decide the election.

"Anyone who's responsible for that many deaths should not remain president of the United States of America," Biden said.

Trump defended his approach to the outbreak and claimed the worst of the pandemic was in the past.

"We're rounding the corner," said Trump, who has played down the virus for months. "It's going away."

Several US states reported record single-day increases in COVID-19 infections on Thursday, evidence the pandemic is accelerating anew.

After an opening segment on the pandemic, Thursday's clash pivoted to rapid-fire exchanges over whether either candidate had improper foreign entanglements.

Trump repeated his accusations that Biden and his son Hunter engaged in unethical practices in China and Ukraine. No evidence has been verified to support the allegations, and Biden called them false and discredited.

Trump's effort to uncover dirt on Hunter Biden's Ukraine business ties led to the president's impeachment. The president and his children have been accused of conflicts of interest of their own since he entered the White House in 2017, most involving the family's international real estate and hotel businesses.

Biden defended his family and said unequivocally he had never made "a single penny" from a foreign country before pivoting to accuse Trump of trying to distract Americans.

"There's a reason why he's bringing up all this malarkey," Biden said, looking directly into the camera. "It's not about his family and my family. It's about your family, and your family's hurting badly."

Biden faulted Trump for avoiding responsibility for the pandemic.

"I take full responsibility," Trump responded. "It's not my fault that it came here, it's China's fault."

Trump claimed on Thursday that a vaccine was close to ready, saying approval would be announced within weeks before acknowledging it was not a guarantee. Most experts say a vaccine is unlikely to be widely available until mid-2021.

Relatively few voters have yet to make up their minds and Trump's window to influence the outcome may be closing. A record 47 million Americans already have cast ballots, eclipsing total early voting from the 2016 election.

After the contentious first debate, Trump passed up another planned debate last week after it was switched to a virtual format following his COVID-19 diagnosis.

On Thursday, the commission that oversees the debate removed plexiglass barriers separating the candidates after Trump provided proof he had tested negative for COVID-19, a source said.

The commission also muted the candidates' microphones to allow each to deliver two-minute statements on each new topic before turning them back on, in an effort to avoid the chaos of the first debate.

Australian Associated Press