Trump’s post came hours after Harris secured the Democratic party’s presidential nomination as party standard bearer in November’s election.
Trump’s White House bid was turned upside down on July 21 when President Biden, 81, facing growing concerns about his age and lagging polling numbers, withdrew his candidacy and backed Harris.
Recall, Biden bowed out following a disastrous debate performance against Trump in June.
A second Trump-Biden televised debate had been scheduled for September 10 on ABC television.
That was expected to remain in place, with Harris replacing Biden, but Trump’s spokesman Steven Cheung last week said it was inappropriate to schedule it before Harris was formally the Democratic nominee.
In his post Trump gave details of the debate venue and the moderators, saying it would be held before a full audience.