With the Capitol towering behind them, several women who said they had been among Jeffrey Epstein’s victims shared harrowing stories of sexual abuse, pleading with members of Congress to demand that the Trump administration release all of its investigative files in the case.

Lawmakers in both parties stood behind them, vowing to keep the pressure on for the disclosures.

Even one of Mr. Trump’s closest allies, Representative Marjorie Taylor Greene of Georgia, said the files must come out.

None of it appeared to be enough to outweigh the pressure from Mr. Trump and Republican leaders, who have moved quickly to squelch legislation that would require the Justice Department to quickly and completely release what it uncovered about Mr. Epstein, the disgraced financier and convicted sex offender who died in prison in 2019 while awaiting trial on sex trafficking charges.

Momentum was flagging behind an effort by Representatives Thomas Massie, Republican of Kentucky, and Ro Khanna, Democrat of California, to force the House to vote on the measure, after most Republicans who initially said they would back it fell in line with the president’s exhortations to let the issue die.

Even as Mr. Epstein’s accusers spoke at the Capitol, some of them growing emotional as they recounted their experiences, Mr. Trump at the White House dismissed the effort to get more files released as a “Democrat hoax that never ends.”

Hours later, House Republicans united to push through an alternative measure backed by Speaker Mike Johnson that directed the House Oversight Committee to continue an investigation into the handling of the Epstein case that it started weeks ago after being forced to do so by Democrats. No such resolution was needed to authorize the inquiry, which is already underway.