US President Donald Trump has rejected a plan to change the rules for his next debates against Democratic rival Joe Biden after the pair’s first match-up was marred by constant interruptions and outbursts.

But Mr Trump’s campaign said it was still planning to turn up.

“Why would I allow the Debate Commission to change the rules for the second and third Debates when I easily won last time?” Mr Trump asked in a tweet on Thursday (local time).

The Commission on Presidential Debates said it would change the rules after Mr Trump repeatedly interrupted Mr Biden and moderator Chris Wallace in a chaotic encounter in Cleveland on Tuesday.

The commission – a non-profit organisation established by both main political parties – said it would adopt changes to allow for a “more orderly discussion” before the next debate in Miami on October 15. There was immediate speculation that this could include a mute button to limit interruptions.

Tuesday’s 90-minute face-off in Cleveland triggered widespread criticism of Mr Trump and, to a lesser extent, Mr Biden. Mr Trump repeatedly attempted to bulldoze over Mr Biden speaking and questioned his intelligence, while Mr Biden called Mr Trump a racist, a liar and the worst president the US had had.

Tweet from @realDonaldTrump

But a Biden aide said his campaign had raised nearly $US10 million ($A14 million) during the debate, adding to the Democrat’s financial advantage with five weeks to go until the November 3 election.

The former US vice president has held a modest but steady lead in national voter surveys for months. However, opinion polls in the battleground states that traditionally decide elections show a closer contest.

On Wednesday Mr Biden went on a whistle-stop train tour through Ohio and Pennsylvania, concluding the day with remarks attacking Mr Trump for his handling of the coronavirus pandemic.

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Mr Biden urged Americans to vote for him in large numbers to eliminate any possibility of Mr Trump trying to stay in the White House if he lost the election.

At Tuesday’s debate, Mr Trump refused again to commit to accepting the election result. He reasserted unfounded complaints that an increase in mail-in ballots because of the coronavirus pandemic would lead to widespread voting fraud.

“The President will step down. The American people will not stand for it. No agency would stand for that happening,” Mr Biden said on a campaign stop.

Also on Wednesday, Mr Trump attempted to distance himself from the right-wing Proud Boys group after declining to denounce white supremacists during the debate.

He said the Proud Boys should “stand back and stand by”, before switching to an attack on the Antifa leftist group,

“I don’t know who the Proud Boys are. I mean, you’ll have to give me a definition, because I really don’t know who they are. I can only say they have to stand down, let law enforcement do their work,” he said at the White House on Wednesday.

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The Trump campaign accused the organisation of “moving the goalposts and changing the rules in the middle of the game.”

Mr Trump also was critical of moderator Wallace, a long-time Fox News anchor, who spent much of the debate trying to restore order.

“Chris had a tough night,” Mr Trump posted on Twitter, calling the debate a “two on one” fight.

On Wednesday, Mr Biden said he hoped organisers of future debates would be able to turn off the microphone of the candidate who is not speaking.

“It was a national embarrassment,” he said of the debate and Mr Trump’s performance. “I am not going to speculate what happens at the second or third debate.”

The debate commission defended Wallace, thanking him “for the professionalism and skill he brought to last night’s debate” and promising “additional tools to maintain order.”

An estimated 73.1 million people tuned in to the face-off on Tuesday night across 16 networks, down from the 84 million who watched the first debate between Mr Trump and Democratic rival Hillary Clinton in 2016.

-with AAP