Days after the Justice Department asked a federal judge to unseal grand jury testimony related to the disgraced financier Jeffrey Epstein, Republicans and Democrats suggested on Sunday that the move was insufficient and called for the release of more information.

“I think it’s a good start,” Representative Tim Burchett, Republican of Tennessee, said in an interview on CNN. But he still wanted to see as many files as possible released, he added later.

President Trump has been contending with fierce criticism from some of his supporters over his administration’s handling of materials related to the sex trafficking investigations of Mr. Epstein and his connections to rich and powerful figures on the left and right. Mr. Epstein died by suicide in 2019 while in federal prison awaiting trial on sex-trafficking charges.

Mr. Trump and many of his allies vowed to release a trove of files in the case, including a so-called “client list” that many involved in the case insist never existed. But the release of some documents earlier this year offered no new revelations. And the Justice Department said this month that it had closed the case and would not release more documents, concluding that there was no client list.

One of Mr. Epstein’s former lawyers, Alan Dershowitz, said in an interview on “Fox News Sunday” that the grand jury testimony was unlikely to contain the information that has most interested Mr. Trump’s supporters.

Mr. Trump has encouraged his base to move on. But the backlash seemed to be on his mind on Sunday morning, when he accused “Radical Left Democrats” of exposing the “Jeffrey Epstein Hoax.”