“Mark my words, I think he is going to try to kick back the election somehow, come up with some rationale why it can’t be held,” Mr. Biden said at a fund-raiser, according to a news media pool report. Mr. Trump, he suggested, is “trying to let the word out that he’s going to do all he can to make it very hard for people to vote. That’s the only way he thinks he can possibly win.”

It was an extraordinary claim for the presumptive Democratic nominee to make about an opponent, especially for Mr. Biden, a former vice president and Washington veteran who prides himself on civility and respect for American institutions, including and especially the presidency.

But as early polls show that Mr. Trump is vulnerable in several key battleground states, and as the president dispenses conflicting and often misleading information at his daily briefings on the coronavirus, Mr. Biden’s remarks amounted to a warning shot that attempts to frame for the public — to his advantage — what may be the ugliest election in recent American history.

“It very much is reflecting the fear that a lot of people have about how President Trump is going to respond later in the year to this election, especially if he continues to see his polls drop, and if he continues to flail and lash out,” said Chuck Hagel, who served as defense secretary in the Obama administration and before that as a Republican senator from Nebraska, and who hosted Mr. Biden at a fund-raiser this month.

Mr. Hagel said he had heard widespread concerns “about what President Trump may pull, especially if he sees he’s losing.”