The plot surrounding the resignation of CIA chief David Petraeus over an extramarital affair thickened Sunday amid reports that his alleged lover had sent emails to a second woman she viewed as a threat to her love interest.

The affair came to light as the FBI was investigating whether a computer used by Petraeus -- a married father of two -- had been compromised, the New York Times and other US media reported, citing government officials.

NBC News and other media reported the Federal Bureau of Investigation was focusing on Paula Broadwell, co-author of a favorable biography of Petraeus, for possible improper access to classified information.

Unnamed officials told the Times that Petraeus's lover was Broadwell, a former Army major who spent long periods interviewing Petraeus for her book.

Broadwell, who is married herself and has two small children, offered no public comment on the revelations.

The Times and The Washington Post, citing an official briefed on the case, reported Saturday that the probe had been triggered by "harassing" emails sent by Broadwell to an unidentified second woman.

The recipient of the emails was so frightened, The Post reported, that she went to the FBI for protection and to help track down the sender.

According to the Post, the second woman did not work at the CIA and her relationship with Petraeus remains unclear. However, the e-mails indicated that Broadwell perceived her as a threat to her relationship with the top spymaster, the paper said.

While Obama praised Petraeus as he acknowledged his departure, there was no denying it added to his headache over the makeup of his future administration, already expected to lose heavyweights such as Secretary of State Hillary Clinton.

Obama had no inkling Petraeus was about to leave until Thursday morning and refused to accept his resignation straight away, the New York Times reported.

"He was surprised, and he was disappointed," the Times quoted one senior administration official as saying. "You don't expect to hear that the Thursday after you were re-elected."

According to the paper, White House officials were only informed of the matter late Wednesday, a day after the election.

A senior intelligence official told the Times that US director of national intelligence James Clapper learned of the situation on Tuesday and had told Petraeus that "the right thing to do" would be to resign.

As he heads into his second term, Obama will likely have to replace not only Clinton, but also Defense Secretary Leon Panetta and Treasury Secretary Tim Geithner.

Speculation is already rife about who will succeed Clinton, who has stressed she wants to reclaim a private life put on hold by decades in the spotlight.

-- Search for Replacement Expected to Be Daunting --

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Now, adding to the rumor mill is talk of who might follow in the footsteps of Petraeus, a 60-year-old former paratrooper credited with turning around the Iraq war.

His deputy Michael Morell will serve as acting CIA director, and is expected to fill in for Petraeus at an upcoming congressional hearing about the CIA's alleged failure to protect a US consulate in Libya from a deadly September 11 attack that left four Americans dead, including Ambassador Chris Stevens.

One name being floated as a possible Petraeus replacement is John Brennan, the White House counter-terrorism adviser and a CIA veteran who has played an instrumental role in Obama's drone war against Al-Qaeda militants.

Others, according to the Wall Street Journal, include Michael Vickers, undersecretary of defense for intelligence, and Congressman Michael Rogers, a Republican who heads the House Permanent Select Committee on Intelligence.

"It needs to be someone who has a lot of credibility... and doesn't have a partisan reputation," Georgetown University professor Stephen Wayne told AFP.

Wayne also floated the name of former Republican senator Chuck Hagel but said his guess would be that Morell will stay put permanently if he does well in the interim.

The most celebrated military officer of his generation, Petraeus took over at the CIA a little more than a year ago. He was credited by some with rescuing a failing US war effort in Iraq in 2007, after then president George W. Bush ordered a surge of troops into the country.

Obama later asked Petraeus to lead a similar surge of US forces in Afghanistan in 2010, leaving a top post as commander of all US forces in the Middle East to do so.

His military background, however, sometimes clashed with the CIA's culture and there was some friction with the congressional committees that oversee the spy services.

In this case, however, the liaison raises potential security concerns in light of Petraeus's highly sensitive position.

Still, the journal Foreign Policy, in a blog post, called his downfall a "huge loss for the United States."

"Petraeus's exit leaves a bitter taste. We all make mistakes. Here's hoping he makes a comeback," it said.