Trump added that he "easily" held victory at the first presidential debate against Biden in Cleveland, citing polls.
Earlier on Thursday, the president's office said Trump wants to participate in the next debate but does not want the rules changed simply to "cover for his rival's inability to perform".
The first debate was widely criticised, mostly because moderator Chris Wallace failed to take control of the debate. As a result, it turned into a spat, with Trump and Biden insulting each other and not covering every issue properly.
The first debate, held on Tuesday in Cleveland was marred by insults and frequent mutual interruptions. The organisers said that they may amend the rules of the show to give the moderator more tools to enforce the order.
There will be two more debates between Trump and Biden, on 15 October in Miami and 22 October in Nashville, and a single round for their running mates. Vice President Mike Pence and Senator Kamala Harris, are scheduled to meet on 7 October in Salt Lake City.