WASHINGTON (AP) — Members of Congress said Sunday they want to know more details about the FBI investigation that revealed an extramarital affair between ex-CIA Director David Petraeus and his biographer, questioning when the retired general popped up in the FBI inquiry, whether national security was compromised and why they weren't told sooner.

"We received no advanced notice. It was like a lightning bolt," said Democratic Sen. Dianne Feinstein of California, who heads the Senate Intelligence Committee.

The FBI was investigating harassing emails sent by Petraeus biographer and girlfriend Paula Broadwell to a second woman. That probe of Broadwell's emails revealed the affair between Broadwell and Petraeus. The FBI contacted Petraeus and other intelligence officials, and Director of National Intelligence James Clapper asked Petraeus to resign.

A senior U.S. military official identified the second woman as Jill Kelley, 37, who lives in Tampa, Fla., and serves as an unpaid social liaison to MacDill Air Force Base in Tampa, where the military's Central Command and Special Operations Command are located.

Staffers for Petraeus said Kelley and her husband were regular guests at events he held at Central Command headquarters.

In a statement Sunday evening, Kelley and her husband, Scott, said: "We and our family have been friends with Gen. Petraeus and his family for over five years. We respect his and his family's privacy and want the same for us and our three children."

A U.S. official said the coalition countries represented at Central Command gave Kelley an appreciation certificate on which she was referred to as an "honorary ambassador" to the coalition, but she has no official status and is not employed by the U.S. government.

The official, speaking on condition of anonymity because he wasn't authorized to discuss the case publicly, said Kelley is known to drop the "honorary" part and refer to herself as an ambassador.

The military official, who spoke on condition of anonymity because he was not authorized to publicly discuss the investigation, said Kelley had received harassing emails from Broadwell, which led the FBI to examine her email account and eventually discover her relationship with Petraeus.

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A former associate of Petraeus confirmed the target of the emails was Kelley, but said there was no affair between the two, speaking on condition of anonymity to discuss the retired general's private life. The associate, who has been in touch with Petraeus since his resignation, says Kelley and her husband were longtime friends of Petraeus and wife, Holly.

Attempts to reach Kelley were not immediately successful. Broadwell did not return phone calls or emails.

Petraeus resigned while lawmakers still had questions about the Sept. 11 attack on the U.S. Consulate and CIA base in Benghazi, Libya, that killed four Americans, including U.S. Ambassador Chris Stevens. Lawmakers said it's possible that Petraeus will still be asked to appear on Capitol Hill to testify about what he knew about the U.S. response to that incident.

Rep. Peter King, chairman of the House Homeland Security Committee, said the circumstances of the FBI probe smacked of a cover-up by the White House.

"It seems this (the investigation) has been going on for several months and, yet, now it appears that they're saying that the FBI didn't realize until Election Day that General Petraeus was involved. It just doesn't add up," said King, R-N.Y.

Petraeus, 60, quit Friday after acknowledging an extramarital relationship. He has been married 38 years to Holly Petraeus, with whom he has two adult children, including a son who led an infantry platoon in Afghanistan as an Army lieutenant.

Broadwell, a 40-year-old graduate of the U.S. Military Academy and an Army Reserve officer, is married with two young sons.

Petraeus' affair with Broadwell will be the subject of meetings Wednesday involving congressional intelligence committee leaders, FBI deputy director Sean Joyce and CIA deputy director Michael Morell.

Petraeus had been scheduled to appear before the committees on Thursday to testify on the attack in Benghazi. Republicans and some Democrats have questioned the U.S. response and protection of diplomats stationed overseas.

Morell was expected to testify in place of Petraeus, and lawmakers said he should have the answers to their questions. But Feinstein and others didn't rule out the possibility that Congress will compel Petraeus to testify about Benghazi at a later date, even though he's relinquished his job.

"I don't see how in the world you can find out what happened in Benghazi before, during and after the attack if General Petraeus doesn't testify," said Sen. Lindsey Graham, R-S.C.

Graham, who is a member of the Senate Armed Services Committee, wants to create a joint congressional committee to investigate the U.S. response to that attack.

Feinstein said she first learned of Petraeus' affair from the media late last week, and confirmed it in a phone call Friday with Petraeus. She eventually was briefed by the FBI and said so far there was no indication that national security was breached.

Still, Feinstein called the news "a heartbreak" for her personally and U.S. intelligence operations, and said she didn't understand why the FBI didn't give her a heads up as soon as Petraeus' name emerged in the investigation.

"We are very much able to keep things in a classified setting," she said. "At least if you know, you can begin to think and then to plan. And, of course, we have not had that opportunity."

Clapper was told by the Justice Department of the Petraeus investigation at about 5 p.m. on Election Day, and then called Petraeus and urged him to resign, according to a senior U.S. intelligence official who spoke on condition of anonymity because he was not authorized to discuss the investigation publicly.

FBI officials say the committees weren't informed until Friday, one official said, because the matter started as a criminal investigation into harassing emails sent by Broadwell to another woman.

Concerned that the emails he exchanged with Broadwell raised the possibility of a security breach, the FBI brought the matter up with Petraeus directly, according to the official, who spoke on condition of anonymity because he was not authorized to publicly discuss the investigation.

Petraeus decided to quit, though he was breaking no laws by having an affair, officials said.

Feinstein said she has not been told the precise relationship between Petraeus and the woman who reported the harassing emails to the FBI.

Georgia Sen. Saxby Chambliss, the top Republican on the Senate intelligence committee, called Petraeus "a great leader" who did right by stepping down and still deserves the nation's gratitude. He also didn't rule out calling Petraeus to testify on Benghazi at some point.

"He's trying to put his life back together right now and that's what he needs to focus on," Chambliss said.

King appeared on CNN's "State of the Union." Feinstein was on "Fox News Sunday," Graham spoke on CBS' "Face the Nation," and Chambliss was interviewed on ABC's "This Week."

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Associated Press writers Michele Salcedo, Pete Yost and Matthew Lee contributed to this report.