Nunes: I know you are but what am I Paul Ryan: What, me worry?

In a statement, a spokesman for Mr. Nunes, Jack Langer, did not dispute that the committee had leaked the messages, but called the premise of this article “absurd.”

“The New York Times, a prominent purveyor of leaks, is highlighting anonymous sources leaking information that accuses Republicans of leaking information,” he said. “I’m not sure if this coverage could possibly get more absurd.”

AshLee Strong, a spokeswoman for Mr. Ryan, declined to comment. In his meeting with the senators, Mr. Ryan made clear that he heard their complaints but noted that he did not run the committee himself, the officials briefed on the encounter said.

The text messages were leaked just days after the same House Republicans had taken the extraordinary step of publicly releasing, over the objections of the F.B.I., a widely disputed memorandum based on sensitive government secrets. Taken together, the actions suggested a pattern of partisanship and unilateral action by the once-bipartisan House panel.

Fox News published the text messages, which were sent via a secure messaging application, in early February. President Trump and other Republicans loyal to him quickly jumped on the report to try to discredit Mr. Warner, suggesting that the senator was acting surreptitiously to try to talk with the former British spy who assembled a dossier of salacious claims about connections between Mr. Trump, his associates and Russia.

“Wow! -Senator Mark Warner got caught having extensive contact with a lobbyist for a Russian oligarch,” Mr. Trump wrote at the time. “Warner did not want a ‘paper trail’ on a ‘private’ meeting (in London) he requested with Steele of fraudulent Dossier fame.”

“All tied into Crooked Hillary,” Mr. Trump added.

The messages between Mr. Warner and Adam Waldman, a Washington lawyer, show that the senator tried for weeks to arrange a meeting with the former spy, Christopher Steele. The Senate committee has had difficulty making contact with Mr. Steele, whom it views as a key witness. And Mr. Waldman, who knew Mr. Steele, presented himself as a willing partner.

Over the summer, Mr. Nunes dispatched Mr. Patel and another member of the committee’s Republican staff to London, where they showed up unannounced at the offices of Mr. Steele, a former British intelligence official.

Told Mr. Steele was not there, Mr. Patel and Douglas E. Presley, a professional staff member, managed to track him down at the offices of his lawyers. There, they said they were seeking only to establish contact with Mr. Steele, but were rebuffed and left without meeting him, according to two people with knowledge of the encounter.

A senior official for the Republican majority on the Intelligence Committee, who spoke on the condition of anonymity because he was not authorized to speak about the matter, said the purpose of the visit had been to make contact with Mr. Steele’s lawyers, not Mr. Steele. Still, the visit was highly unusual and appeared to violate protocol, because they were trying to meet with Mr. Steele outside official channels.

Ordinarily, such a visit would be coordinated through lawyers, conducted with knowledge of the House Democrats, who were not informed and the American Embassy.

In the months since, Mr. Patel has apparently forged connections at the White House. In November, he posted a series of photos to Facebook of him and several friends wearing matching shirts at the White House bowling alley. “The Dons hit the lanes at 1600 Pennsylvania,” Mr. Patel wrote under the photos.