Mr. Clinton and Mr. Epstein were first linked in 2002, when it was reported that the former president took his first of four trips aboard Mr. Epstein’s private jet, for a trip related to Mr. Clinton’s work on his foundation, according to a Clinton spokesman, and Mr. Clinton has stressed that he has not been in touch with Mr. Epstein in over a decade.

But Mr. Trump has his own long history with Mr. Epstein, one he has been playing down since before he began his presidential campaign. The two New Yorkers were friends through the 1990s, and into the 2000s, and in at least one instance, were even caught on camera ogling women together at Mar-a-Lago, Mr. Trump’s Palm Beach, Fla., estate. The source of their eventual falling out — which Mr. Trump has highlighted more than the friendship itself — has been in dispute.

Whether he believes the theories he promotes or not, Mr. Trump knows that many people will latch onto them, lured by the idea that a hidden force is controlling fate.

“He revels in conspiracy theories because he knows it gives him quick and easy traction with the masses — they’re easily swayed by the notion that there is an organized group getting over on them,” said Timothy L. O’Brien, a journalist and one of Mr. Trump’s biographers. “Because he never feels remorse or guilt about peddling these fables, he dives right in even when he knows better.”

On Saturday, when the news of Mr. Epstein’s death broke, Mr. Trump was at his New Jersey golf club, where he plans to spend his vacation and where, accompanied by few aides, he often uses Twitter more freely than when he is at the White House.

“It’s another example of something where he should stop and think about the fact that he’s the president of the United States, and stop his thumbs, but he never does,” said Rich Lowry, a columnist and editor of the conservative National Review.

In the murky story of Mr. Epstein’s death, Mr. Trump found particularly fertile soil: the demise of an accused pedophile with powerful friends, whose apparent suicide in a federal Manhattan jail has raised questions about “serious irregularities” and has many people — not just Mr. Trump — speculating in public about what might have really taken place.