US Republican presidential nominee Donald Trump proposed to debate Democratic Vice President Kamala Harris on Fox News on 4 September, and the Harris campaign responded saying Mr Trump is trying to back out of a debate that had been set to run on ABC.
The rules would be similar to the first debate with US President Joe Biden, who has since dropped his re-election bid, Mr Trump said in a post on Truth Social late on Friday.
However this time it would have a "full arena audience" and take place in the battleground state of Pennsylvania, Mr Trump said.
A second Biden-Trump debate had been agreed for the 10 September on ABC News that the former US president had suggested should be moved to Fox.
Ms Harris, who on Friday secured the delegate votes needed to clinch the democratic nomination, said that she plans to attend the originally planned debate.
"It's interesting how 'any time, any place' becomes 'one specific time, one specific safe space,'" she wrote on X.
"I'll be there on 10 September like he agreed to. I hope to see him there."
The Spokesperson for Ms Harris, Michael Tyler, said Mr Trump is "running scared" and that her campaign is happy to discuss further debates after the 10 September one that "both campaigns have already agreed to."
The former US president said on social media that the ABC debate "has been terminated in that Biden will no longer be a participant" and because he is in litigation with ABC.
The Trump campaign did not immediately respond to a request for comment about the Harris campaign's remarks.
Recent polls show a tight contest between Ms Harris and Mr Trump, who had enjoyed a bigger lead over Biden after the first debate.
ABC News had no comment about whether the republican presidential candidate had dropped out of the debate, a spokesperson said.
Fox News did not immediately respond to a request for comment.
Mr Trump's proposal for the debate on Fox came right after the Democratic National Committee launched an advertising campaign taunting him by saying "the convicted felon is afraid to debate" and questioning whether that is due to his stance on abortion.
