WASHINGTON — The FBI investigation that led to the resignation of CIA Director David Petraeus started with a complaint several months ago that Paula Broadwell, his biographer and paramour, was sending harassing emails to a third person, a U.S. official told The Associated Press.

FBI agents discovered exchanges between Broadwell, a West Point graduate and Army Reserve officer, and Petraeus, the retired four-star general who commanded troops in Iraq and Afghanistan, that revealed they were having an affair, according to the official.

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Paula Broadwell, David Petraeus’ biographer and mistress, says she first met him in the spring of 2006. The Associated Press

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Investigators said the emails raised the possibility of security breaches that needed to be addressed directly with Petraeus because his emails in the matter were in most instances from a personal account, rather than his CIA one.

Details about the third person were not immediately available.

The official was not authorized to publicly discuss about the investigation and spoke about the probe only on condition of anonymity.

The sudden and unexpected end of a career that many thought might culminate in a run for the presidency came on Friday. Petraeus admitted to an extramarital affair in tendering his resignation, which President Obama accepted.

Petraeus’ deputy, Michael Morell, will serve as acting director, Obama said. Morell was the key CIA aide in the White House to President George W. Bush during the terrorist attacks of Sept. 11, 2001.

The change in leadership is taking place as the administration and the CIA struggle to defend security and intelligence lapses before the Sept. 11 attack that killed the U.S. ambassador to Libya and three others Americans. It was an issue during the presidential campaign that ended with Obama’s re-election Tuesday.

Petraeus, who turned 60 on Wednesday, has been married for 38 years to Holly Petraeus; they met when he was a cadet at the U.S. Military Academy at West Point, N.Y. She was the daughter of the academy superintendent. They have two children, and their son led an infantry platoon in Afghanistan.

The retired general told CIA employees in a statement that he was guilty of “extremely poor judgment” in engaging in the affair. “Such behavior is unacceptable, both as a husband and as the leader of an organization such as ours.” He said he had offered his resignation to Obama on Thursday and the president accepted it Friday.

Administration officials said the White House was first notified about the Petraeus affair on Wednesday, the day after the election. Obama, who returned to the White House that evening after spending Election Day in Chicago, wasn’t informed until Thursday morning.

For the director of the CIA, being engaged in an extramarital affair is considered a serious breach of security and a counterintelligence threat. If a foreign government had learned of the affair, the reasoning goes, Petraeus or Broadwell could have been blackmailed or otherwise compromised. Military justice considers conduct like an extramarital affair to be possible grounds for court-martial.

Failure to resign also could create the perception for the rank and file that such behavior is acceptable.

Petraeus, who became CIA director in September 2011, was known as a shrewd thinker and hard-charging competitor.

In the preface to “All In: The Education of General David Petraeus,” published by Penguin in January, Broadwell said she first met Petraeus in the spring of 2006. She was a graduate student at the Kennedy School of Government at Harvard, and he was visiting the university to discuss his experiences in Iraq and a new counterinsurgency manual he was working on.

In 2008, she wrote, she was pursuing a Ph.D. in public policy and embarking on a case study of Petraeus’ leadership. After Obama put Petraeus in charge in Afghanistan in 2010, Broadwell decided to expand her research into an authorized biography.

Broadwell made many trips to Afghanistan, with unprecedented access to Petraeus, and also spent time with his commanders across the country. When Petraeus took the job at the CIA, she remained in close contact with him, sometimes invited to his office for events like meeting with actress Angelina Jolie.

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