“We don’t know whether there were U.S. persons involved, but it is our responsibility to find out,” Mr. Schiff said in an interview on MSNBC. “And I don’t think anyone on the committee, or our chairs in the House or Senate, ought to be stating a conclusion or deeming it their responsibility to push back on unfavorable press stories.”

The divide has grown starker since The Washington Post reported on Friday that the White House had enlisted Mr. Nunes as part of an effort to push back on a story this month by The New York Times. The Times report focused on contacts between Russian intelligence officials and Trump associates and campaign aides.

In an interview that aired Friday on HBO’s “Real Time with Bill Maher,” Representative Darrell Issa, Republican of California, said that a special prosecutor should be appointed to investigate Russian meddling in the election. The statement from Mr. Issa was notable, as he is a hard-line Republican who was one of President Obama’s biggest critics.

On Monday, Mr. Issa again called for an independent review. “The American people need a cleareyed view of the nefarious actions of the Russian government,” Mr. Issa said.

The issue of lawmakers helping the administration was also a point of contention in the Senate on Monday. The minority leader, Senator Chuck Schumer, Democrat of New York, sharply criticized Senator Richard Burr, the Republican chairman of the Senate Intelligence Committee, who has acknowledged helping the Trump administration push back on the story. Mr. Burr and the intelligence committee’s top Democrat, Senator Mark Warner of Virginia, are also conducting an investigation into Russia.

“Senator Burr is on notice, because what he did was wrong,” Mr. Schumer said. “This is not the way to conduct a fair, impartial investigation that goes where the facts lead.”

Republicans and Democrats who set out to work together on politically charged investigations often end up refusing to cooperate with each other. From 2014 to 2016, Democrats repeatedly clashed with Republicans who were leading an investigation into the attacks on an American outpost in Benghazi, Libya. And in 2014, Republicans refused to sign on to the findings of a five-year investigation by the Senate Intelligence Committee into the C.I.A.’s use of torture and deceit in its detention program.

At his news conference, Mr. Nunes said the ”major crimes” that have taken place during the Trump administration were government leaks to the media about national security matters, including transcripts of conversations the president has had with the leaders of Mexico and Australia.