The campaign of Democratic presidential candidate Kamala Harris has accepted the rules of next week's debate against Republican Donald Trump, including microphones being muted when it is not a candidate's turn to speak, a source familiar with the matter said on Wednesday.

The debate would be the first between Trump and Harris, who took over as the Democratic candidate from President Joe Biden following his decision to step aside on July 21 after a faltering debate performance in late June against the former president.

The source, who declined to be identified, said the Harris campaign was still hoping for moments where ABC News, which will host the Sept. 10 debate, is forced to unmute the mics and let the candidates respond.

Harris' rise to the top of the Democratic ticket has re-energized a Democratic campaign that had harbored doubts about Biden's chances.

Polls showed that Trump had built a lead over Biden but Harris has since edged ahead of the Republican candidate in some national opinion polls.

Over the weekend, Harris called on Trump to debate her with their microphones switched on throughout the event.

So-called "hot mics" can help or hurt political candidates, catching off-hand comments that sometimes were not meant for the public. Muted microphones also prevent the debaters from interrupting their opponent.

Trump senior adviser Jason Miller said he was thrilled that Harris and her team had accepted the rules.

"Americans want to hear both candidates present their competing visions to the voters, unburdened by what has been," he said. "No notes, no sitting down, no advance copies of the questions."

Democratic vice presidential candidate Tim Walz and Republican vice presidential candidate JD Vance have also agreed to an Oct. 1 debate on CBS News.