Mr. Holder has said little publicly about the investigation. The F.B.I. director, James B. Comey, asked by reporters in December why it was taking so long, said: “I can’t say. I mean, I guess I could say, but I won’t say.”

Marc Raimondi, a Justice Department spokesman, declined to comment on the investigation.

At a news conference shortly after Mr. Petraeus resigned, President Obama said he had no evidence that Mr. Petraeus had disclosed classified information “that in any way would have had a negative impact on our national security.”

“We are safer because of the work that Dave Petraeus has done,” Mr. Obama said, referring to his career in government. “And my main hope right now is — is that he and his family are able to move on and that this ends up being a single side note on what has otherwise been an extraordinary career.”

But investigators concluded that, whether or not the disclosure harmed national security, it amounted to a significant security breach in the office of one of the nation’s most trusted intelligence leaders. They recommended that Mr. Petraeus face charges, saying lower-ranking officials had been prosecuted for far less.

Federal agents stumbled onto the affair after Jill Kelley, a friend of Mr. Petraeus’s, complained to the F.B.I. that she had received anonymous threatening emails about her relationship with Mr. Petraeus. F.B.I. agents opened a cyberstalking investigation, traced the message to Ms. Broadwell and began searching her emails. That is when they discovered evidence that she and Mr. Petraeus were having an affair.

Mr. Petraeus is said to have begun the affair with Ms. Broadwell in 2011, soon after taking the job at the C.I.A. and while she was interviewing him for her book, “All In: The Education of General David Petraeus.”

Mr. Petraeus resigned from the C.I.A. three days after Mr. Obama was re-elected. In a brief statement, Mr. Petraeus admitted to the affair, saying that “after being married for over 37 years, I showed extremely poor judgment.”