Ammunition Management for More Obtainability Act of 2013 - Prohibits a federal agency, other than the Department of Defense (DOD), during the six-month period beginning on the enactment of this Act, from purchasing during any month or possessing at any one time more rounds of ammunition than the monthly average of rounds of ammunition purchased by the agency between January 1, 2001, and December 31, 2009. Directs the Comptroller General (GAO) to report to Congress on federal agency purchasing of ammunition.