Mr Trump refused to participate in the second event, planned for October 15, after it was announced the debate would be held virtually.
“I’m not going to do a virtual debate,” Mr Trump told Fox News, calling the decision “ridiculous” moments after the Commission on Presidential Debates announced the changes.
Looking to avoid the disruptions that marred the first meeting, organisers have announced that the October 22 debate will feature a mute button to allow each candidate to speak uninterrupted during their opening statements.
The Trump campaign voiced objections to the change, but said the president would still take part. It is one of Mr Trump’s last chances to reach a large prime-time audience before voting ends.
The coronavirus pandemic has drastically changed how the Republican and Democratic presidential campaigns are being fought this year, meaning the debates have taken on even more significance than in previous years.
Read more: Election 2020 polls
When, where and what time are the debates?
September 29, Ohio
The first presidential debate between Mr Trump and Mr Biden was a chaotic squabble between the two candidates.
The rivals ripped chunks out of each other on their records and issues such as the economy, coronavirus and racism.
Mr Trump was rebuked several times by Chris Wallace, the moderator, for speaking over his opponent. At one point, after incessant interruptions from the president, Mr Biden said: “Will you shut up, man?”
Read more: Who won the US election debate?
October 7, Utah