Asked whether he would “commit here today for a peaceful transferral of power after the November election,” Mr. Trump demurred, passing on a chance to call for a calm and orderly election process.

“We’re going to have to see what happens,” he told a reporter during a news conference at the White House. “You know that I’ve been complaining very strongly about the ballots, and the ballots are a disaster.”

“I understand that, but people are rioting,” responded the reporter, Brian Karem of Playboy magazine, who repeated the question.

“Get rid of the ballots and you’ll have a very peaceful — there won’t be a transfer, frankly. There will be a continuation,” the president said. That was an apparent reference to mail-in ballots, which for months he has railed against, without evidence, as rife with fraud and likely to produce a delayed, tainted or outright illegitimate election result.

Mr. Trump’s refusal — or inability — to endorse perhaps the most fundamental tenet of American democracy, as any president in memory surely would have, was the latest instance in which he has cast grave uncertainty around the November election and its aftermath. Democrats are growing increasingly alarmed as Mr. Trump repeatedly questions the integrity of the vote and suggests that he might not accept the results if he loses.

Earlier on Wednesday, Mr. Trump said he needed to swiftly confirm a successor for Justice Ruth Bader Ginsburg because he expected disputes over the election result to be resolved by the Supreme Court, which could split 4-to-4 if a ninth justice is not seated.

“He’s threatening the election process and saying out loud what everyone has assumed he’s been thinking,” said Julian E. Zelizer, a professor of American political history at Princeton University. “The more he makes these arguments, the more he normalizes the fact that this can be part of the conversation.”

“Even if meant to distract, these are powerful words to come from a president,” Mr. Zelizer added. “He’s clearly accelerating his effort to set up a challenge to an outcome that is unfavorable to him.”