Will Hurd, a former C.I.A. clandestine officer and now a Republican representative from Texas, said that Grizzly Steppe, the American code name given to Russia’s efforts to disrupt the 2016 election, had worked. “Russian intelligence will consider ‘Grizzly Steppe’ to be their most successful covert action operation because it created a wedge, whether real or perceived, between the U.S. president, intelligence community and the American public,” he said.

Others were less certain that Mr. Trump’s recent comments on Twitter would have a significant impact.

“The C.I.A. is not going to stop providing intelligence to the president of the United States because he said some negative things,” said Michael Hurley, a former C.I.A. operations officer.

But, he said, “people function better when they know their work is valued.”

The challenge for Mr. Pompeo may be getting Mr. Trump simply to pay attention to whatever the C.I.A. finds out. The president-elect has yet to sit down regularly for the daily briefings that the intelligence agencies prepare, and he has repeatedly brushed off the need to do so once in office.

Mr. Pompeo, though, is close to Vice President-elect Mike Pence, who does sit for a daily intelligence briefing. The hope at the agency is that working through Mr. Pence will give Mr. Pompeo the kind of direct line to the Oval Office that the C.I.A. has come to expect — and will keep intelligence from being filtered through Lt. Gen. Michael T. Flynn, Mr. Trump’s choice for national security adviser, a retired intelligence officer who has been a harsh critic of the C.I.A. as overly political.

On Thursday, Mr. Pompeo said he did not believe that politics regularly seeped into the work done at the C.I.A., though he did say that politicians had at times sought to twist intelligence for their own purposes.

Though Mr. Pompeo is known for his unrelenting partisanship in Congress — he has maintained that Hillary Clinton was involved in a cover-up after the 2012 attacks on the American consulate in Benghazi, Libya — both Democrats and Republicans have said they believe he is capable of rising above the political fray to lead the C.I.A.