By Donald Judd, CNN

(CNN) — President Donald Trump “would not recommend” a special prosecutor to investigate the Jeffrey Epstein case, White House press secretary Karoline Leavitt said Thursday — despite some GOP calls to do so.

“The president would not recommend a special prosecutor in the Epstein case. That’s how he feels,” Leavitt told reporters at a White House briefing, adding that she was “not sure” if Trump had discussed appointing a special counsel with Attorney General Pam Bondi.

The president dodged on Wednesday when asked if he’d consider appointing a special counsel to investigate the Epstein affair, telling CNN at the White House: “I have nothing to do with it.”

The appointment of a special counsel falls under the purview of the attorney general and the Department of Justice, which usually has limited interactions with the White House to avoid the appearance of political impropriety. But Trump has eschewed the traditional independence afforded to the DOJ.

He’s ordered the investigation and prosecution of his political enemies and even proclaimed himself the “chief law enforcement officer in our country” during a March speech at the department — a title traditionally used to refer to the attorney general.

But when it comes to Epstein, Trump has been more publicly deferential to Bondi. He’s repeatedly said she can release any more information she deems “credible” in the investigation into the sex offender. Pressed on whether Trump should order the release of all the Epstein files, Leavitt said Thursday the decision is “out of the president’s control.” And the press secretary wouldn’t say if Trump has been briefed by Bondi on unreleased details from the Epstein files, telling CNN’s Kristen Holmes: “Not to my knowledge, and that’s a question for the attorney general.”

Last week, the Department of Justice announced in an unsigned memo that there is no evidence that Epstein kept a “client list” or was murdered. That provoked many of Trump’s own supporters, especially after Bondi had previously suggested in interviews that the client list was sitting on her desk. The attorney general said last week that, at the time, she was referring to other files related to the Epstein investigation, not a client list specifically.

That memo, and the efforts to quash speculation around further incriminating evidence linking Epstein to prominent high-profile individuals, did little to quell rampant speculation and increased calls for transparency from many of Trump’s most vocal supporters. The president on Wednesday called people who have fixated on the files “weaklings” who have bought into a “hoax.”

Far-right activist and Trump confidant Laura Loomer told Politico Sunday that the administration should appoint a special counsel “to do an independent investigation of the handling of the Epstein files,” adding she does not believe Bondi “has been transparent or done a good job handling this issue.”

Republican Rep. Lauren Boebert has also called for a special counsel, telling conservative podcaster Benny Johnson in an interview: “I think moving forward, we need a special counsel. That has got to happen. There has to be a special investigation into this if we aren’t going to be provided information.”

In an interview with conservative pundit John Solomon that aired Wednesday, the president lumped the Epstein case with other law enforcement matters that have annoyed him, including prior special counsel investigations into him and his campaign. He suggested an FBI examination of those things could also include the Epstein case.

“I think they could look at all of it. It’s all the same scam. They could look at this Jeffrey Epstein hoax also, because that’s the same stuff,” Trump said.