By Phil Stewart and Idrees Ali

WASHINGTON (Reuters) - U.S. Defense Secretary Ashton Carter has decided not to impose further punishment on David Petraeus, a former U.S. military commander and CIA director who admitted sharing classified information with his mistress, according to a letter seen by Reuters.

The short letter was sent by Stephen Hedger, the assistant secretary of defense for legislative affairs, and the decision is in line with an Army review.

Petraeus resigned as head of the CIA in 2012 after it was revealed that he was having an affair with his biographer, Army Reserve officer Paula Broadwell. When he pleaded guilty to mishandling classified information, a court document signed by Petraeus and prosecutors said that in 2011, Petraeus illegally gave Broadwell access to official binders.

In April, the retired four-star general was sentenced to two years of probation and fined $100,000 but was spared prison time after pleading guilty to mishandling classified information.

The Pentagon could have sought to further reprimand Petraeus under military law.

Hedger's letter was addressed to Senate Armed Service Committee Chairman Senator John McCain and Senator Jack Reed, who had recently asked Carter not to take further action.

The Pentagon declined to comment on the letter.

Petraeus, a counter-insurgency expert with a Princeton University doctorate, served as the top U.S. commander in the wars in Iraq and Afghanistan and was once considered a possible vice presidential or presidential candidate.

Known as "black books," the binders that Petraeus shared with Broadwell contained classified information including identities of covert officers, code word information, war strategy, intelligence capabilities, diplomatic talks and information from high-level White House National Security Council meetings, according to court records.

Petraeus now serves as chairman of the private equity firm Kohlberg Kravis Roberts' captive economic and geopolitical think tank, the KKR Global Institute, according to its website.

(Reporting by Phil Stewart and Idrees Ali; Editing by Bernard Orr and Bill Trott)