New emails showed that Mr. Summers, a former Harvard president, had stayed in touch with Jeffrey Epstein for years after Mr. Epstein faced sex trafficking charges.
Mr. Summers, a former treasury secretary, had sought money from Mr. Epstein for a poetry foundation led by his wife, Elisa New, an emerita Harvard literature professor.
The president has reversed himself and encouraged lawmakers to vote for compelling the Justice Department to turn over investigation documents, but he never really needed their approval.
President Trump said on Monday that he would sign a bill related to the release of the full Epstein files should it reach his desk after passing the House and Senate.
Faced with a mass defection on a bill to demand the release of the Epstein files, the president rushed to avoid an embarrassing loss, suggesting a slip in his iron grip on the G.O.P.
Demonstrators outside the Capitol last week. As Republicans gear up for midterm elections and some begin to plot a future after Mr. Trump, the Epstein episode is a rare instance in which he has lost control.