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.

"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's 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 James Clapper, the director of national intelligence, asked Petraeus to resign.

A senior U.S. military official has 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.

Kelley and her husband were regular guests at events held at Central Command headquarters, aides to Petraeus said.

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 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.

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.

Extramarital relationship

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's 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 Republican Senator Lindsey Graham, R-S.C.

Feinstein said she learned of Petraeus's 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 has been no indication that national security was breached.

News 'a heartbreak'

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's 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.

The committees weren't informed until Friday, one FBI 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.