"It will not be a third debate", he writes in capital letters in the post.
The US presidential candidates met in a debate on Tuesday night Swedish time. Trump claims that opinion polls "clearly show" that he won the debate.
However, Harris' odds improved with bookmakers after the two met in the TV broadcast. And in an opinion poll from Reuters /Ipsos, 53 percent of those who say they have at least heard something about the debate think Harris won, while the corresponding figure for Trump is 24, according to the survey.
67 million people in the US watched the debate, according to the measurement company Nielsen. Kamala Harris said afterwards that she would be happy to meet Trump in another debate.
In October, the two vice presidential candidates JD Vance, Republicans, and Tim Walz, Democrats, will meet to debate on TV.
Donald Trump did significantly better in the debate against Joe Biden, when the latter was still the Democratic presidential candidate. On the night of June 28, the two met in a TV debate where Biden's performance was described as shaky and incoherent. Less than a month later, Biden dropped out of his election campaign.
The presidential election in the US will be held on November 5.
