The request comes after a congressional committee released thousands of documents that raised new questions about Trump's relationship with the convicted sex offender.
Along with Clinton, who socialised with the late financier in the early 2000s, Trump said he had asked the Justice Department to investigate former Treasury Secretary Larry Summers and Reid Hoffman, the LinkedIn founder who is also a prominent Democratic donor.
"Epstein was a Democrat, and he is the Democrat's problem, not the Republican's problem!" he wrote on social media.
"They all know about him, don't waste your time with Trump. I have a Country to run!"
The Justice Department did not immediately respond to a request for comment.
JPMorgan in an emailed statement said: "We regret any association we had with the man, but did not help him commit his heinous acts. We ended our relationship with him years before his arrest on sex trafficking charges."
Trump and Epstein were friends during the 1990s and the 2000s but Trump says he broke off ties before Epstein's 2008 conviction.
Still, the steady release of documents highlighting the relationship has proven to be a headache during his second term in office.
JPMorgan paid $US290 million ($A444 million) in 2023 to some of Epstein's victims to settle accusations that it had turned a blind eye to his sex trafficking.
The other people named by Trump could not immediately be reached for comment.
No credible evidence has surfaced that Trump or any of people named by the US president on Friday were involved in Epstein's sex trafficking, and all have previously denied wrongdoing.
Clinton flew on Epstein's private jet several times before the financier's 2008 conviction while Summers accepted philanthropic gifts from Epstein as president of Harvard University.
Hoffman has acknowledged meeting with Epstein multiple times in professional situations.
All three men have expressed regret about their relationship with him.
Before his 2008 conviction, Epstein worked and socialised with a long list of well-known figures, including the UK's former Prince Andrew, who was stripped of his royal title due in part to his association with Epstein.
While nine in 10 Republicans say they approve of Trump's performance in the White House overall, just four in 10 say they approve of his handling of the Epstein files, according to a Reuters/Ipsos poll conducted in October.
