Leading advisers for both Donald Trump and Hillary Clinton are raising the prospect of the GOP nominee skipping the remaining debates for 2016, following the candidates' performance on Monday night.

After the first debate, former New York City Mayor Rudy Giuliani blasted debate moderator Lester Holt of NBC. Giuliani, a Trump adviser, said he thought the GOP nominee ought to consider not attending the next debate.

"If I were Donald Trump I wouldn't participate in another debate unless I was promised that the journalist would act like a journalist and not an incorrect, ignorant fact checker," Giuliani told reporters per Politico. "The moderator would have to promise that there would be a moderator and not a fact checker and in two particular cases an enormously ignorant, completely misinformed fact checker."

The Clinton campaign, meanwhile, expressed anxiety that Trump would choose to ditch the debates altogether.

"We're very worried his campaign will be meeting tomorrow and say, 'What's a way we can get out of these last two debates?'" said Clinton campaign chairman John Podesta to NBC.

It would not be unusual for Trump to skip the next debate or threaten to do so. Trump dodged a GOP primary debate before the Iowa caucus, and later cited the decision as harmful to his performance in the Hawkeye State.

Two more presidential debates are scheduled for October. Clinton and Trump will met in St. Louis on Oct. 9 and in Las Vegas on Oct. 19. The vice presidential nominees running with Clinton and Trump will debate in Virginia next Tuesday.