Kamala Harris on Saturday challenged Donald Trump to another debate in the lead-up to the US presidential election, with her campaign saying she had accepted an invitation from broadcaster CNN to host the event on October 23.

"Vice President Harris is ready for another opportunity to share a stage with Donald Trump," her campaign chair Jen O'Malley Dillon said in a statement.

"The American people deserve another opportunity to see Vice President Kamala Harris and Donald Trump debate before they cast their ballots."

Republican Trump has attended two debates so far, one against President Joe Biden and one against Harris, who has since replaced her boss at the top of the Democratic ticket.

Trump has previously rejected the idea of facing Harris again. His campaign did not immediately respond to a request for comment.

Most pundits put Harris as the winner of the last debate, which was held on September 10.

Biden's poor debate performance against Trump in June, where the president struggled to complete some of his sentences, catalysed concerns over his age and ramped up pressure for the 81-year-old to drop out of the race.

The move has left Trump, 78, now the oldest presidential nominee against a much younger Harris, 59.

Saturday's announcement came as three states – Virginia, Minnesota and South Dakota – have already begun early voting in what is an agonisingly close race.

On the campaign trail on Friday, Harris cast Trump and his party as "hypocrites" over abortion, blaming Trump for an abortion ban in the battleground state of Georgia that she said had caused the deaths of two women.

Trump has frequently bragged on the campaign trail that his three Supreme Court picks paved the way for the 2022 overturning of the national right to abortion, turning the issue over to state governments.

At least 20 states have since brought in full or partial restrictions, with Georgia banning most abortions after six weeks of pregnancy.

The race remains neck-and-neck, with Trump running with the support of a conservative religious voter base and others, many of whom feel disaffected by the country's political status quo.

Hardline anti-immigrant rhetoric has become a centerpiece of his election campaign.

The race between Harris and Trump has continued despite a tense atmosphere that was brought to the fore last weekend when a gunman appeared to have tried to assassinate Trump in Florida, the second such threat in as many months.

Every vote will count in the race, whose result Trump has once again refused to say he will accept if he loses.

The former president faces criminal charges for allegedly trying to overturn the 2020 result, after which his supporters violently stormed the US Capitol on January 6, 2021.

The result is expected to hinge on just seven crucial swing states, including Georgia.

Trump on Friday sought to lay the blame for any potential loss at the door of Jewish American voters, sparking outrage.

"If I don't win this election... in my opinion the Jewish people would have a lot to do with a loss," Trump told an anti-Semitism event on Thursday, repeating his grievance that Jewish voters have historically leaned towards the Democrats.

He is set to campaign on Saturday in North Carolina. (AFP)