The rules would be similar to the first debate with President Joe Biden, who has since dropped his re-election bid, Trump said in a post on Truth Social late on Friday. 

But this time it would have a "full arena audience" and take place in the battleground state of Pennsylvania, Trump said.

Trump and Biden had agreed to a second debate on September 10 on ABC News that the former president had suggested should be moved to Fox.

Harris, who on Friday secured the delegate votes needed to clinch the Democratic nomination, said on Saturday 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 September 10, like he agreed to. I hope to see him there."

Harris spokesman Michael Tyler said Trump is "running scared" and that her campaign is happy to discuss further debates after the September 10 one that "both campaigns have already agreed to".

On Saturday, Trump said on Truth Social that Harris is "afraid to do it" and that he will see her on September 4, "or, I won't see her at all".

Recent polls show a tight contest between Harris and Trump, who had enjoyed a bigger lead over Biden after the first debate.

ABC News had no comment about whether Trump had dropped out of the debate, a spokesperson said.

Fox News did not immediately respond to a request for comment.

Trump's proposal for the debate on Fox came right after the Democratic National Committee launched an advertising campaign on Friday taunting him by saying "the convicted felon is afraid to debate" and questioning whether that is due to his stance on abortion.

David Plouffe, an adviser to former president Barack Obama who recently joined the Harris campaign, said on X "Now, he seems only comfortable in a cocoon, asking his happy place Fox to host a Trump rally and call it a debate. Maybe he can only handle debating someone his own age."

Trump is 78 and Harris is 59.

With AAP.