The push for the release of the investigative files held by the Department of Justice was led by Republican Thomas Massie, a Kentucky congressman who sometimes dissents from his party, and Democrat Ro Khanna, a California congressman, both of whom introduced the legislation.
Massie has faced criticism from Trump for his push to release the files, but has stood firm.
“In 2030, he’s not going to be the president,” Massie said to ABC News over the weekend. He added that fellow Republicans who voted against release "will have voted to protect paedophiles”.
Another Republican who has pushed for the release of the files is House Representative Marjorie Taylor Greene. She had been a staunch supporter of Trump before the two fell out over the issue, with the president now calling her a "traitor".
At a news conference earlier in the day on Tuesday, Greene said she was speaking up on behalf of Epstein's survivors.
"Let me tell you what a traitor is. A traitor is an American that serves foreign countries and themselves; a patriot is an American that serves the United States of America and Americans like the women standing behind me," Greene said.
She said that the row over Epstein has been one of the "most destructive things" to Trump's Make America Great Again movement since his election in 2016.
Survivors of Epstein’s abuse also spoke at the news conference, urging lawmakers to release the files and pushing Trump to do the same.
Epstein survivor Annie Farmer said that keeping the files under wraps amounted to “institutional betrayal”.
“Because these crimes were not properly investigated, so many more girls and women were harmed,” Ms Farmer said.