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week of Oct. 21, and she acknowledged the affair, a government official briefed on the matter said. She also voluntarily gave the agency her computer. In a search, the agents discovered several classified documents, which raised the additional question of whether Mr. Petraeus had given them to her. She said that he had not. Agents interviewed Mr. Petraeus the following week. He also admitted to the affair but said he had not given any classified documents to her. The agents then interviewed Ms. Broadwell again on Friday, Nov. 2, the official said.

Based on that record, law enforcement officials decided there was no evidence that Mr. Petraeus had committed any crime and tentatively ruled out charges coming out of the investigation, the official said. Because the facts had now been settled, the agency notified James R. Clapper, the director of national intelligence, about 5 p.m. on the following Tuesday -- Election Day.

Meanwhile, the F.B.I. agent who had helped get a preliminary inquiry started, and learned of Mr. Petraeus's affair and the initial concerns about security breaches, became frustrated. Apparently unaware that those concerns were largely resolved, the agent alerted the office of Representative Eric Cantor, Republican of Virginia, the House majority leader, about the inquiry in late October. Mr. Cantor passed on the agent's concerns to Mr. Mueller.

Officials said Sunday that the timing of the notifications had nothing to do with the election, noting that there was no obvious political advantage for either President Barack Obama or Mitt Romney in the news that the C.I.A. director had had an affair; Mr. Petraeus has been highly regarded by both Republicans and Democrats. They also said that Mr. Cantor's call to the F.B.I. on Oct. 31 had not accelerated or otherwise influenced the investigation, which they said had never stalled.

F.B.I. and Justice Department officials knew their handling of the case would ultimately receive immense scrutiny and took significant time to determine whom they were legally required to inform, according to a senior law enforcement official.

"This was very thought-through," the official said.

The law requires that the Senate and House intelligence committees be kept "fully and currently informed" of intelligence activities, which conceivably might cover an investigation into a possible compromise of the C.I.A. director's e-mail account and the possession of classified documents by Ms. Broadwell.

But Justice Department and F.B.I. rules, designed to protect the integrity of investigations and the privacy of people who come under scrutiny, say that investigators should not share potentially damaging information about unproven allegations or private matters unless it is critical for the investigation.

Glenn A. Fine, the inspector general for the Justice Department from 2000 to 2011, said it appeared that the F.B.I. was "legitimately following a lead" about possible criminal wrongdoing or a security breach.

"Some have said the F.B.I. was out to get the C.I.A.," said Mr. Fine, who is now a partner at the law firm Dechert in Washington. "That might have been true 20 years ago. But it is hard to believe that is going on today."

John Prados, a historian and an author on intelligence and its abuses, said the case "posed several dilemmas for the F.B.I." that would have prompted agents and their bosses to proceed gingerly.

"Petraeus is a very important person, so they would want to be crystal-clear on exactly what happened and what the implications were," Mr. Prados said. "There was probably a sense that it had to be taken to top bureau officials. And bureau officials probably thought they had better tell the White House and Congress and the D.N.I., or they might get in trouble later," he added, referring to the director of national intelligence.

But if the security issues were resolved and no crime had been committed, Mr. Prados said, there was no justification for informing Congress or other agencies that Mr. Petraeus had had an affair. "In my view, it should never have been briefed outside the bureau," he said.