Giuliani added that the Department of Justice is “very motivated to get to the bottom of it.”

His morning tweet made no mention of Trump, who on Saturday retweeted a message from conservative actor and comedian Terrence K. Williams. Williams suggested that Epstein’s death might be tied to Clinton, who once socialized with Epstein. Williams also questioned how Epstein could have died by suicide if he had been on suicide watch.

Williams’s claim is completely unsubstantiated, and federal officials say Epstein was not on suicide watch at the time of his death. He had been placed on suicide watch last month but then taken off within a week, according to a person familiar with the situation, who spoke on the condition of anonymity to discuss a matter that is the subject of an ongoing investigation.

Angel Ureña, a Clinton spokesman, responded on Twitter over the weekend: “Ridiculous, and of course not true — and Donald Trump knows it. Has he triggered the 25th Amendment yet?”

The 25th Amendment spells out a process for the president’s Cabinet to remove him from office.

The Justice Department, which is part of Trump’s administration, initially said that Epstein died by “apparent suicide” in a special housing unit of the Metropolitan Correctional Center in New York City.

Giuliani, a former mayor of New York, seemed to cast doubt on that explanation Saturday in a separate tweet.

“It is inconceivable Epstein could have hung himself if there was a suicide Watch,” he wrote, adding: “Follow the motives.”

News of Epstein’s death on Saturday quickly fed conspiracy theories that powerful people who once socialized with Epstein — including Trump, as well as Clinton — had a hand in the financier’s fate and stood to benefit from his silencing.

Lynne Patton, a Trump appointee at the Department of Housing and Urban Development, also used her Instagram account to spread a version of a conspiracy theory.