Tuesday’s opening debate in Cleveland quickly turned chaotic, with frequent interruptions by the candidates — particularly Mr Trump.
The Commission on Presidential Debates (CPD) said on Wednesday that it “intends to ensure that additional tools to maintain order are in place for the remaining debates”.
The commission and representatives from Mr Trump’s and Mr Biden’s campaigns met on Wednesday morning to discuss the previous night’s debate and potential changes.
But the commission, which has organised every general election debate since 1988, did not specify what changes it is considering.
Mr Trump tweeted on Thursday that he opposed any changes. “Why would I allow the Debate Commission to change the rules for the second and third Debates when I easily won last time,” he tweeted shortly after landing in New Jersey, where he was to hold a campaign fundraiser at his private golf club.
On a conference call with reporters, Mr Trump’s re-election campaign indicated that he would attend the remaining debates regardless of whether the rules are changed.
“We’re ready to move on to the second and third debates,” said campaign communications strategist Jason Miller. “There shouldn’t be any changes. We don’t want any changes.”
Andrew Bates, a spokesman for Mr Biden, said “we will participate under the CPD’s rules”.
Organisers and both campaigns expect that the next presidential debate, a “town meeting” set for October 15 in Miami, will be more orderly, as the candidates address questions asked directly to them by voters.
The third and final debate, set for October 22 in Nashville, is slated to feature a similar format to Tuesday’s event.