Defense Secretary Ash Carter will not seek to demote retired Gen. David Petraeus for sharing classified information with his biographer, according to a Jan. 29 letter from the Pentagon to Sen. John McCain (R-Ariz.).

"As you know, the Army completed its review of his case and recommended no additional action. Given the Army review, Secretary Carter considers this matter closed," Stephen C. Hedger, principal deputy assistant secretary of Defense for legislative affairs, wrote in a letter obtained by The Hill.

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The letter was in response to one written to Carter by McCain, chairman of the Senate Armed Services Committee, and Sen. Jack Reed (D-R.I.), ranking member, urging him not to retroactively demote Petraeus after reports that he was considering it.

A defense official confirmed the letter's authenticity but declined further comment.

Reports emerged that Carter was considering the move in order to be consistent in his treatment of senior officers who engage in misconduct and to send a message that no one is above punishment.

However, the retroactive demotion of Petraeus would come more than four years after the misconduct, and despite the retired general already being convicted and sentenced a fine of $100,000 and two years of probation.

While he was still serving, Petraeus shared two notebooks of notes containing classified information with his biographer, with whom he admitted having an extramarital affair.

The then-retired four-star resigned as CIA director in 2011 after the affair came to light.

-- Updated 7:40 p.m.