The woman who received the e-mails was Jill Kelley in Tampa, Fla., according to law enforcement officials. The nature of her relationship with Petraeus is unknown.
When Petraeus’s name surfaced, FBI investigators were concerned that the CIA director’s personal e-mail account had been hacked and that national security had been threatened. The officials said further investigation, including FBI interviews with Broadwell and Petraeus, led to the discovery that the two were engaged in an affair.
The law enforcement officials said the e-mails indicated that Broadwell perceived the other woman as a threat to her relationship with Petraeus.
Attempts to reach Broadwell and her relatives have been unsuccessful, and she has not made a public statement since she was linked with Petraeus on Friday.
All three senior officials who described the impetus for the investigation spoke on the condition of anonymity because aspects of the inquiry are ongoing.
Petraeus, a retired four-star Army general who was once seen as a potential presidential candidate, said Friday that he was resigning as CIA chief because he had been involved in an extramarital affair. He has been married for 38 years and has two grown children, though he said in his resignation statement to CIA colleagues that he had been married “over 37 years.”
Broadwell is married and has two young children.
In an e-mail sent to a longtime friend Friday night, Petraeus expressed regret for letting down his family and the nation. The friend, who described the contents of the e-mail on the condition of anonymity, said Petraeus conveyed profound remorse in the message.
“He was deeply sorry for the pain he has caused his family,” the friend said. “He also noted how much he loved his job at the agency. He said he really relished the intellectual challenge there.”
Other details emerged Saturday indicating that the Petraeus allegations became a secret election-night drama for the Obama administration. That evening, the Justice Department informed the director of national intelligence, James R. Clapper Jr., that their investigation had unearthed compromising information about the CIA director, according to a senior U.S. intelligence official.
Clapper then spoke with Petraeus and urged him to resign, notifying the White House the next day. That sequence has become a source of controversy, raising questions among some members of Congress about why key intelligence committees were not notified earlier and why the FBI waited before informing the administration about a probe that had stumbled onto embarrassing details about the CIA chief.