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The rules would be similar to the first debate with President Joe Biden, who has since dropped his reelection 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 Sept. 10 on ABC News which the former president had suggested should be moved to Fox, the most popular network with his followers.
Harris, who on Friday secured the delegate votes needed to clinch the Democratic nomination for the Nov. 5 election, said on Saturday that she plans to participate in the originally planned debate.
"It’s interesting how 'any time, any place' becomes 'one specific time, one specific safe space,'" she wrote on social media platform X. "I’ll be there on Sept. 10, like he agreed to. I hope to see him there."
Harris spokesperson Michael Tyler said Trump is "running scared" and that her campaign is happy to discuss further debates after the Sept. 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 Sept. 4, "or, I won't see her at all."
On Friday he said that the ABC debate had been "terminated" in that Biden would no longer be in it and because he himself was in litigation with ABC.
ABC on July 26 outlined qualification requirements for the debate but did not mention any candidates by name.
Requirements include proving polling support and state ballot access by Sept. 3.
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, posted on social media: "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.
Former Democratic President Jimmy Carter, who turns 100 on Oct. 1, said, "I'm only trying to make it to vote for Kamala Harris," the Atlanta Journal-Constitution reported on Saturday.