A top House committee released more than 33,000 pages of records on Tuesday that the Justice Department had turned over last month in connection with its investigation of the disgraced financier Jeffrey Epstein, as Republican leaders toiled to tamp down pressure in their ranks for more transparency.

The release of the files by the House Oversight Committee, the chamber’s chief investigative panel, had been expected, and it was not immediately clear whether it included any material the Trump administration had not already made public. Mr. Epstein, whose rich and powerful friends included President Trump, died by suicide in prison in 2019 while awaiting trial on sex trafficking charges.

After years of alluding to a potential cover-up in the case, Mr. Trump has faced a backlash from his right-wing base over the Justice Department’s decision to close the investigation without revealing all of what was discovered. The Oversight panel subpoenaed all the files, but the department has turned over only a portion of them.

The publication of what it received came as Congress returned from a five-week recess that House Republican leaders had hoped might dissipate the fervor over the Epstein files, only to find that pressure had intensified.

On Tuesday afternoon, Representative Thomas Massie, Republican of Kentucky, pushed forward with a bipartisan measure that would force a vote on the House floor on whether to demand that the administration publicly release all of its investigative material on Mr. Epstein.

Representative Robert Garcia of California, the top Democrat on the Oversight Committee, said in a statement that 97 percent of the documents published on Tuesday had been previously released and accused Republicans of trying to “give cover” to Mr. Trump by feigning transparency.