President Trump announced Thursday night that he was authorizing Attorney General Pam Bondi to seek the public release of grand jury testimony from the prosecution of the disgraced financier Jeffrey Epstein, and Ms. Bondi said she would make that request in federal court on Friday.

Mr. Trump, under intense pressure from his right-wing base after a Justice Department review found no evidence to support conspiracy theories about the sex trafficking case, ordered Ms. Bondi to “produce any and all Grand Jury Testimony, subject to Court approval,” in a social media post.

The president cited “the ridiculous amount of publicity given to Jeffrey Epstein” for his directive, which falls far short of demands from some congressional Republicans to make public all investigative files collected by the department and the F.B.I., not just testimony presented in federal court.

Ms. Bondi, a Trump loyalist accused by far-right influencers of abetting a cover-up, responded immediately with a post on social media that undercut the memo the department and F.B.I. drafted this month declaring Mr. Epstein’s 2019 jailhouse death a suicide and the case closed.

“President Trump — we are ready to move the court tomorrow to unseal the grand jury transcripts,” she wrote, quickly reversing course at his command. But it was not clear that she would succeed, because the secrecy of grand jury transcripts is highly protected.

Mr. Trump’s request came hours after The Wall Street Journal reported on a 50th birthday greeting it said Mr. Trump sent Mr. Epstein in 2003, including a sexually suggestive drawing, an expression of friendship and a reference to secrets they shared.