Potentially dozens of Republicans have now signalled they are willing to break ranks and vote in favour of a bill that would compel the US government to publish all the documents on Epstein and the criminal investigations into him that it holds.
Supporters of the bill appear to have enough votes for it to pass the House this week, though it is unclear whether it would pass in the Senate, the other chamber of the US Congress.
Epstein, a financier, was found dead in his New York prison cell in 2019, in what a coroner later ruled a suicide. He was being held on charges of sex trafficking, having previously been convicted of soliciting prostitution from a minor in 2008.
The two criminal investigations into Epstein amassed a vast trove of documents including transcripts of interviews with victims and witnesses, and items confiscated from raids of his various properties. The material that has not yet been made public is often referred to as the Epstein files.
Trump repeated White House dismissals of the attention over the files as a Democrat-led "hoax" to "deflect" attention away from his party's work.
"The Department of Justice has already turned over tens of thousands of pages to the Public on 'Epstein,' are looking at various Democrat operatives (Bill Clinton, Reid Hoffman, Larry Summers, etc.) and their relationship to Epstein, and the House Oversight Committee can have whatever they are legally entitled to, I DON'T CARE!," he wrote on his Truth social platform.
He added that he wanted Republicans to "get BACK ON POINT".
Republican House Speaker Mike Johnson made a similar point on Sunday, saying calls to release the files were the "entire game plan" for opposition Democrats.
"Trump has clean hands," Johnson told Fox News. "He's not worried about it. I talk to him all the time. He has nothing to do with this. He's frustrated that they're turning it into a political issue."