WASHINGTON — David Petraeus has resigned as director of the CIA after admitting he had an extramarital affair.

According to his letter of resignation, Petraeus asked President Barack Obama on Thursday to allow him to resign and today the president accepted.

Petraeus said in a statement that he had shown “extremely poor judgment” in having the affair.

Petraeus has been married for 37 years to Holly Petraeus, whom he met when he was a cadet at the U.S. Military Academy at West Point.

The retired four-star general led the military campaigns in Iraq and Afghanistan, then took the helm of the CIA in September 2011.

The CIA had no immediate comment.