WASHINGTON — David Petraeus, the director of the CIA and one of America’s most decorated four-star generals, resigned Friday after an FBI investigation uncovered evidence that he had been involved in an extramarital affair.

Petraeus, 60, issued a statement acknowledging the affair after President Barack Obama accepted his resignation and it was announced by the CIA on Friday.

Government officials said that the FBI began investigating a “potential criminal matter” several months ago that was not focused on Petraeus. In the course of their inquiry into whether a computer used by Petraeus had been compromised, agents discovered evidence of the relationship as well as other security concerns. About two weeks ago, FBI agents met with Petraeus to discuss the investigation.

Administration and congressional officials identified the woman with whom he was having the affair as Paula Broadwell, the author of a biography of Petraeus. Her book, All In: The Education of General David Petraeus, was published this year. Broadwell could not be reached for comment.

Broadwell, a graduate of the U.S. Military Academy at West Point, spent 15 years in the military, according to a biography that had appeared on her website. She spent extended periods of time with Petraeus in Afghanistan, interviewing him for her book, which grew out of a two-year research project for her doctoral dissertation and which she promoted on a high-profile tour that included an appearance on The Daily Show with Jon Stewart. Married with two children, she has described Petraeus as her mentor.

Senior members of Congress were alerted to Petraeus’ impending resignation by intelligence officials about six hours before the CIA announced it. One congressional official who was briefed on the matter said that Petraeus had been encouraged “to get out in front of the issue” and resign and that he agreed.

As for how the affair came to light, the congressional official said: “It was portrayed to us that the FBI was investigating something else and came upon him. My impression is that the FBI stumbled across this.”

The FBI did not inform the Senate and House intelligence committees about the inquiry until this week, according to congressional officials, who noted that by law the panels — and especially their chairmen and ranking members — are supposed to be told about significant developments in the intelligence arena. The Senate committee plans to pursue the question of why it was not told, one official said.

The revelation of a secret inquiry into the head of the nation’s premier spy agency raised urgent questions about Petraeus’ 14-month tenure at the CIA and the decision by Obama to elevate him last year to head the agency after leading the country’s war effort in Afghanistan.

White House officials said they did not know about the affair until this week, when Petraeus informed them.

“After being married for over 37 years, I showed extremely poor judgment by engaging in an extramarital affair,” Petraeus said in his statement, expressing regret for his abrupt departure. “Such behavior is unacceptable, both as a husband and as the leader of an organization such as ours. This afternoon, the president graciously accepted my resignation.”

Petraeus’ admission and resignation represent a fall from grace for one of the most prominent figures in America’s modern military and intelligence community, a commander who helped lead the nation’s wartime activities in the decade after the Sept. 11, 2001, attacks and was credited with turning around the failing war effort in Iraq.

At the CIA, Petraeus maintained a low profile, in contrast to the celebrity that surrounded him as a general.

But since the attack in Benghazi, Libya, that killed four Americans two months ago, critics had increasingly pressured him to give the agency’s account of the chaotic night. Petraeus was scheduled to testify before a closed congressional hearing next week.

White House officials say they were informed Wednesday night that Petraeus was considering resigning because of an extramarital affair. Intelligence officials notified the president’s national-security staff. Obama was at the time on his way back to Washington from Chicago, where he had gone to await election returns.

On Thursday morning, just before a staff meeting at the White House, Obama was told.

“He was surprised, and he was disappointed,” one senior administration official said. “You don’t expect to hear that, the Thursday after you were re-elected.”

The president was in the White House all day Thursday getting back to his old routine after months on the campaign trail. That afternoon, Petraeus came in to see him and informed him that he strongly believed he had to resign.

Obama did not accept his resignation right away.

“He told him, ‘I’ll think about it overnight,’” the administration official said.

After months on the road, the disclosure of a career-killing extramarital affair from his larger-than-life CIA director was the last thing that Obama was expecting, the official said.

The president, officials said, did not want Petraeus to leave. But he ultimately decided that he would not lean heavily on him to stay. On Friday, he called Petraeus and accepted the resignation, “agreeing with Petraeus’ judgment that he couldn’t continue to lead the agency,” a White House official said.

The White House had hoped to keep the news under wraps until after the daily briefing for the media, but as it was reported on MSNBC, reporters checking their e-mail confronted Jay Carney, the press secretary, who tried to duck the questions.

“I think I’ll let Gen. Petraeus address this,” Carney said.

Shortly after the news broke, Obama released a statement praising Petraeus for his “extraordinary service” to the country and expressing support for him and his wife, Holly.

“By any measure, through his lifetime of service, David Petraeus has made our country safer and stronger,” the president said. Without directly addressing the affair, Obama added, “Going forward, my thoughts and prayers are with Dave and Holly Petraeus, who has done so much to help military families through her own work.”

Petraeus’ resignation and the circumstances surrounding it stunned military officers who have served alongside him in war zones over the past two decades and the nationalsecurity establishment he later served.

“It was a punch in the gut for those of us who know him,” said Col. Michael Meese, a professor at West Point who has known Petraeus for a decade and served as one of his top aides in Bosnia, Iraq and Afghanistan.

“Dave’s decision to step down represents the loss of one of our nation’s most respected public servants,” said James Clapper, the director of national intelligence.

By acknowledging an extramarital affair, Petraeus was confronting a sensitive issue for a spy chief. Intelligence agencies are often concerned about the possibility that agents who engage in such behavior could be blackmailed for information.

Petraeus praised his colleagues at the CIA’s headquarters in Langley, Va., calling them “truly exceptional in every regard” and thanking them for their service to the country. He made it clear that his departure was not how he had envisioned ending a storied career in the military and in intelligence.

Petraeus was credited for helping to develop and put in place the “surge” in troops in Iraq that helped wind down the war in that country. Petraeus was moved to Afghanistan in 2010 after Obama fired Gen. Stanley McChrystal over comments he made to a magazine reporter. In Afghanistan, Petraeus led the push for a similar increase in troops ordered by Obama, but he was unable to replicate the success he had in the Iraq conflict. Last year, Obama persuaded Petraeus to leave the Army after 37 years to lead the CIA, succeeding Leon Panetta, who moved to the Defense Department.

In his statement Friday, Obama said that Michael Morell, the deputy director of the CIA, would take over once again as acting director. Morell served in that position briefly after Panetta left the agency last year.

Among those candidates who might replace Petraeus permanently is John Brennan, the president’s adviser for domestic security and counterterrorism. Brennan was considered for CIA director before Obama’s term began but withdrew amid criticism from some of the president’s liberal supporters. Another possibility is Michael Vickers, the top Pentagon intelligence policy official and a former CIA officer who is highly regarded by the White House.

Information for this article was contributed by Peter Baker, Helene Cooper, Michael S. Schmidt, Eric Schmitt and Scott Shane of The New York Times.

Front Section, Pages 1 on 11/10/2012