CIA Director David Petraeus resigned as head of the leading US spy agency on Friday, saying he had engaged in an extramarital affair and acknowledging he "showed extremely poor judgment."

In a letter to the CIA workforce, Petraeus, 60, said he met with

President Barack Obama at the White House on Thursday and asked "to be allowed, for personal reasons, to resign from my position."

"After being married for 37 years, I showed extremely poor judgment by engaging in an extramarital affair," he wrote. "Such behaviour is unacceptable, both as a husband and as the leader of an organization such as ours."

Obama, who was re-elected to a second term on Tuesday, said in a statement he had accepted Petraeus' resignation, praising him for his work at the Central Intelligence Agency and for leading US troops in Iraq and Afghanistan.

Obama said Michael Morell, the agency's long-time deputy director, would serve as acting CIA chief. Morell is a leading candidate to be Petraeus' permanent successor, sources said.

The woman with whom the former CIA director had

the affair is Paula Broadwell, according to a person familiar with the matter. She is an author who wrote a biography of Petraeus titled "All In."

Attempts to reach Broadwell were unsuccessful. There was no answer at the door of her house in the affluent Charlotte, North Carolina, neighbourhood of Dilworth.

Much about the sudden and dramatic turn of events remained unknown Friday evening, including how long the affair had gone on and what prompted Petraeus to resign now, just days after the 2012 presidential election.

There were indications, however, that the affair was first uncovered a few months ago during an investigation by the FBI. A US national security source said the FBI had stumbled across evidence of Petraeus' affair during an apparently unrelated investigation of news leaks.