Declining to elaborate on the specifics of the classified briefing, Mr. Conaway and Mr. Schiff said it had given members of the committee “a valuable opportunity” to follow up on public testimony that Mr. Comey and Admiral Rogers gave in March.
“We remain committed to working with the F.B.I. as they continue their investigation to ensure that no stone is unturned,” the lawmakers said in a joint statement.
It has been more than six weeks since Mr. Comey’s extraordinary confirmation to the committee that the F.B.I. is investigating possible ties between Mr. Trump’s associates and Russia. That hearing, the inquiry’s first, was the committee’s last moment of public comity.
Less than two days later, Mr. Nunes, who was leading the investigation, plunged it into disarray with his assertion that Mr. Trump or his associates may have been incidentally caught up in surveillance of foreigners conducted by American spy agencies. Mr. Trump seized upon the news as vindication of his unfounded claim that Trump Tower in New York was wiretapped by former President Barack Obama.
The investigation, still in its infancy, ground to a halt. After it was revealed that Mr. Nunes obtained his information on White House grounds from White House staff members, Democrats called on him to recuse himself from the inquiry. He eventually did, but only when it emerged that he was under investigation by the House Ethics Committee for possibly leaking classified information. Mr. Conaway, the most senior Republican on the committee, took over.
The encore appearance before the committee by the heads of the F.B.I. and N.S.A. has proved a sticking point. After Mr. Nunes scuttled the public hearing with Ms. Yates and other officials in favor of another round of questions for Mr. Comey and Admiral Rogers, Democrats accused Mr. Nunes of bowing to White House pressure. A series of letters between Ms. Yates’s lawyer and the White House counsel showed that administration officials had tried to block her from testifying before Congress, an accusation the White House spokesman, Sean Spicer, later denied.
Last month, the House committee extended a new invitation to Ms. Yates; James R. Clapper Jr., the former director of national intelligence; and John O. Brennan, the former C.I.A. director.
The panel has not scheduled that public hearing, though Ms. Yates and Mr. Clapper are expected to testify before a Senate panel on Monday.
Days after Mr. Trump took office, Ms. Yates alerted the administration that Michael T. Flynn, then the national security adviser, had misled Vice President Mike Pence and other White House officials about his communications with the Russian ambassador to the United States, and that it could make him vulnerable to blackmail by Russia.
Mr. Flynn, a three-star Army general who was forced out of the administration after less than a month, is now under investigation by the Pentagon’s inspector general over allegations that he failed to disclose payments from a foreign government or get them approved, a potential violation of federal law for a retired military officer.
Thursday was the second visit to the Capitol in two days for Mr. Comey, who testified on Wednesday before senators charged with overseeing the F.B.I. Mr. Comey defended his decision to announce shortly before Election Day that he had reopened the case into Hillary Clinton’s use of a private email server, saying that while it made him “mildly nauseous” to think he affected the election, he believed he had made the right call.
Representative Tom Rooney, Republican of Florida and a former Army lawyer who is assisting Mr. Conaway in leading the inquiry, said on Thursday that the committee had not finished questioning Mr. Comey.
“It’s going to be a very long process, which is fine,” he told reporters as he left the meeting. “It needs to be done right.”
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