Vice President Kamala Harris accepted a CNN invitation to a presidential debate on 23 October, just days before the November election.
Hours later, Donald Trump told supporters that he would not participate, saying it’s “too late”.
The two faced off in a previous debate in Philadelphia on 10 September.
CNN had said an October debate would follow the same format as the June one with President Joe Biden, the then-Democratic candidate, which Trump was largely seen as winning.
In a statement on Saturday, Harris-Walz campaign chair Jen O’Malley Dillon said that Americans “deserve another opportunity” to see Harris and Trump debate before the November election.
“It would be unprecedented in modern history for there to just be one general election debate,” she said. “Debates offer a unique chance for voters to see the candidates side by side and take stock of their competing visions for America.”
On X, formerly Twitter, Harris said that she “gladly” accepted the debate invitation and hoped Trump would also take part.
After the 10 September debate, Trump had said there would be no further debates.
Speaking at a rally in Wilmington, North Carolina on Saturday, he claimed victory in that earlier debate and said “it’s just too late” for another.
“Voting has already started,” he said, accusing Harris of seeking another round of sparring “because she’s losing badly.”
At the Trump rally, some voters told the BBC they hoped another debate would take place – but only under certain conditions.
“If you’re not afraid, why not? They both did great [at the last debate],” said Trump supporter Steve Castellano, adding that he thought the moderators were “a little biased”.
“They should debate again at a network Trump chooses,” he added. “What I would really love is a good podcaster [to moderate]. I’d really love Joe Rogan to do it.”
Harris holds a slight lead over Trump in national polling averages.
Snap polls released immediately after the 10 September debate found that most viewers thought Harris had been the better performer.
Since then, a majority of national polls suggest that Harris has made small gains with voters.
The two candidates exchanged swipes and barbs at the previous debate, with Trump calling Harris a “radical left liberal” and a Marxist who was destroying America.
Harris, for her part, goaded Trump, belittled the size of his rally crowds and quoted his Republican detractors.
CBS, the BBC’s news partner in the US, has also invited both presidential candidates to participate in an October debate in Arizona.