The pair of retweets come on a day when Mr. Trump expressed outrage on Twitter over what he called “dishonest” and “inaccurate” coverage of his presidency by the news media, including The New York Times. Mr. Trump insisted that reports that several survivors of the mass shooting in El Paso last weekend had refused to see him when he visited their hospital on Wednesday were false, but provided no evidence.

Like Mr. Trump, Mr. Clinton had been friendly with Mr. Epstein but broke ties with him many years ago. In a July statement, Mr. Ureña, Mr. Clinton’s spokesman, said that the former president had taken several trips with Mr. Epstein on his private plane in 2002 and 2003 but that the men had not spoken in more than a decade. Mr. Clinton “knows nothing about the terrible crimes” of which Mr. Epstein has been accused and, in one case, had been sentenced, the statement said.

Even before Mr. Trump weighed in on the subject, Senator Marco Rubio, Republican of Florida, said on Twitter that while scrutiny of Mr. Epstein’s death was warranted, “the immediate rush to spread conspiracy theories about someone on the ‘other side’ of partisan divide having him killed illustrates why our society is so vulnerable to foreign disinformation & influence efforts.”

Earlier Saturday, one of the president’s senior appointees at the Department of Housing and Urban Development, Lynne Patton, posted a headline about Mr. Epstein’s death on Instagram, perpetuating a debunked right-wing narrative. Including the comment, “Hillary’d!!” she also referred to Vincent Foster, the Clinton White House counsel who died by suicide in 1994 — a crucial episode in the unfounded theory tying the Clintons to allegedly suspicious deaths.

Adding to the extraordinary nature of Mr. Trump’s retweets was the fact that Mr. Clinton is a former president. American presidents have traditionally treated their predecessors and successors with pronounced respect, even when they are from different parties or ran bitter campaigns against one another. But after defeating Mrs. Clinton in a 2016 campaign during which he suggested he might imprison her, Mr. Trump has repeatedly ridiculed and taunted both Clintons.

Tweeting on another subject earlier in the day, Mr. Trump seemed to criticize joint United States military exercises with South Korea that have enraged North Korea, calling them “ridiculous and expensive.” The president said that the North Korean leader, Kim Jong-un, had offered him “a small apology” for that country’s recent short-range missile tests, which violate United Nations resolutions but which Mr. Trump has brushed off. “I look forward to seeing Kim Jong Un in the not too distant future!” he wrote.