The video above is from an earlier version of this story and will be updated.
In a post on his social media platform, Trump argued that Vice President Kamala Harris could've accepted an offer to debate on Fox News on Sept. 4, or could've negotiated a second debate before the ABC News debate.
"She was a no-show at the Fox Debate, and refused to do NBC & CBS. KAMALA SHOULD FOCUS ON WHAT SHE SHOULD HAVE DONE DURING THE LAST ALMOST FOUR YEAR PERIOD. THERE WILL BE NO THIRD DEBATE!" Trump wrote.
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Harris had challenged Trump to another showdown immediately after Tuesday's matchup in Philadelphia, Pennsylvania.
Harris took the stage at a rally in Charlotte, North Carolina, just after Trump's announcement. Although she did not cite Trump's social media post, Harris said he and she "owe it to the voters to have another debate."
"Two nights ago, Donald Trump and I had our first debate, and I believe we owe it to the voters to have another debate," Harris said. "Because this election and what is at stake could not be more important. On Tuesday night, I talked about issues that I know matter to families across America, like bringing down the cost of living, investing in America's small businesses, protecting reproductive freedom and keeping our nation safe and secure."
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"But that's not what we heard from Donald Trump," she continued. "Instead, it was the same old show, that same tired playbook that we have heard for years, with no plans for how he would address the needs of the American people because, you know, it's all about him, it's not about you. Well, folks, I said it then, I say it now, it's time to turn the page."
ABC News' Will McDuffie, Gabrielle Abdul-Hakim and Fritz Farrow contributed to this report.