Washington — As former President Donald Trump suggested Sunday that he may pull out of the scheduled Sept. 10 presidential debate with Vice President Kamala Harris, the two sides are at odds over whether to allow host ABC News to mute the candidates' microphones when it is not their turn to speak.

For the Harris campaign, it believes Trump's and Harris' microphones should be on throughout the debate, the vice president's spokesperson confirmed. But the Trump campaign is pushing for the same rules regarding microphones in place for the first presidential debate, which was a match-up between President Biden and Trump hosted by CNN in June, according to reports.

Mr. Biden exited the presidential race following the debate after his performance raised concerns about his ability to defeat Trump in November and fitness for a second term. But before the face-off, his campaign laid out its parameters for the debates and said the candidates' microphones should be active only when it is his time to speak.

Politico Playbook first reported the logjam between the Trump and Harris campaigns over microphones.

"We have told ABC and other networks seeking to host a possible October debate that we believe both candidates' mics should be live throughout the full broadcast," Brian Fallon, Harris' spokesperson, confirmed to CBS News. "Our understanding is that Trump's handlers prefer the muted microphone because they don't think their candidate can act presidential for 90 minutes on his own."

Fallon said the Harris campaign suspects Trump's advisers haven't told him about the disagreement over microphones because "it would be too embarrassing to admit they don't think he can handle himself against Vice President Harris without the benefit of a mute button."

"The vice president is ready to deal with Trump's constant lies and interruptions in real time," he continued. "Trump should stop hiding behind the mute button."

But the Trump campaign told CBS News that changes to the debate format are coming from Harris' campaign.

Jason Miller, a senior adviser to the Trump campaign, also told Playbook that Harris' team asked for a "seated debate." But the Harris campaign told CBS News on Monday that is "100% false."

The Republican presidential nominee proposed three debates with Harris: with Fox News on Sept. 4;  ABC News on Sept. 10; and NBC News on Sept. 25. But Harris has only agreed to participate in the ABC-hosted match-up set for Sept. 10.

Still, Trump has suggested more than once that he may back out of the ABC debate. In a social media post on Sunday, the former president criticized an interview by host Jonathan Karl and a panel on its show "This Week" and questioned "why would I do the debate against Kamala Harris on that network?"

But a senior adviser with the Trump campaign says "of course" Trump still wants to participate in the debate.

The former president said earlier this month that he would debate Harris on Fox News on Sept. 4 and said the ABC-hosted debate had been "terminated" since Mr. Biden had ended his bid for reelection. The former president also pointed to a defamation lawsuit he filed against ABC News and host George Stephanopoulos and said it creates a conflict of interest.

Trump also said that a Fox-hosted debate would have a "full arena audience," a departure from the terms of the June debate, which was held with only the candidates and moderators at CNN's television studio in Atlanta.

The vice-presidential nominees, Sen. JD Vance of Ohio and Minnesota Gov. Tim Walz, are set to debate on Oct. 1, which will be broadcast on CBS. 

Ed O'Keefe, Olivia Rinaldi and Aaron Navarro contributed to this report.