The concerns about Mr. Flynn’s vulnerabilities, born from misleading statements he made to White House officials about his conversations with the Russian ambassador, are at the heart of a legal and political storm that has engulfed the Trump administration. Many of Mr. Trump’s political problems, including the appointment of a special counsel and the controversy over the firing of the F.B.I. director, James B. Comey, can ultimately be traced to Mr. Flynn’s stormy tenure.

Time and again, the Trump administration looked the other way in the face of warning signs about Mr. Flynn. Mr. Trump entrusted him with the nation’s secrets despite knowing that he faced a Justice Department investigation over his undisclosed foreign lobbying. Even a personal warning from President Barack Obama did not dissuade him.

Mr. Pompeo sidestepped questions from senators last month about his handling of the information about Mr. Flynn, declining to say whether he knew about his own agency’s concerns. “I can’t answer yes or no,” he said. “I regret that I’m unable to do so.” His words frustrated Senator Ron Wyden, an Oregon Democrat and a member of the Senate Intelligence Committee.

“Either Director Pompeo had no idea what people in the C.I.A. reportedly knew about Michael Flynn, or he knew about the Justice Department’s concerns and continued to discuss America’s secrets with a man vulnerable to blackmail,” Mr. Wyden said in a statement. “I believe Director Pompeo owes the public an explanation.”

After Mr. Pompeo’s Senate testimony, The New York Times asked officials at several agencies whether Mr. Pompeo had raised concerns about Mr. Flynn to the president and, if so, whether the president had ignored him. One administration official responded on the condition of anonymity that Mr. Pompeo, whether he knew of the concerns or not, had not told the president about them.