WASHINGTON — Senior officials across the government became convinced in January that the incoming national security adviser, Michael T. Flynn, had become vulnerable to Russian blackmail.

At the F.B.I., the C.I.A., the Justice Department and the Office of the Director of National Intelligence — agencies responsible for keeping American secrets safe from foreign spies — career officials agreed that Mr. Flynn represented an urgent problem.

Yet nearly every day for three weeks, the new C.I.A. director, Mike Pompeo, sat in the Oval Office and briefed President Trump on the nation’s most sensitive intelligence — with Mr. Flynn listening. Mr. Pompeo has not said whether C.I.A. officials left him in the dark about their views of Mr. Flynn, but one administration official said Mr. Pompeo did not share any concerns about Mr. Flynn with the president.

The episode highlights another remarkable aspect of Mr. Flynn’s stormy 25-day tenure in the White House: He sat atop a national security apparatus that churned ahead, despite its own conclusion that he was at risk of being compromised by a hostile foreign power.