Mr. Petraeus issued a statement acknowledging the affair after President Obama accepted his resignation and it was announced by the C.I.A. The disclosure ended a triumphant re-election week for the president with an unfolding scandal.
Government officials said that the F.B.I. began an investigation into a “potential criminal matter” several months ago that was not focused on Mr. Petraeus. In the course of their inquiry into whether a computer used by Mr. Petraeus had been compromised, agents discovered evidence of the relationship as well as other security concerns. About two weeks ago, F.B.I. agents met with Mr. Petraeus to discuss the investigation.
Administration and Congressional officials identified the woman as Paula Broadwell, the co-author of a biography of Mr. Petraeus. Her book, “All In: The Education of General David Petraeus,” was published this year. Ms. Broadwell could not be reached for comment.