Federal Buildings Energy Savings Act of 2013 - Amends the National Energy Conservation Policy Act to direct each federal agency to implement requirements for the use of energy and water efficiency measures in federal buildings through private financing instead of appropriations, unless: (1) to do so conflicts with the primary mission of the agency or facility, or (2) if greater cost savings can be generated under a different program.

Requires the Secretary of Energy (DOE) to direct agencies to include in energy savings performance contracts appropriate termination clauses for facilities that will or may close before the end of a contract's term.

Includes as an "energy or water conservation measure" under such Act a measure to support the use of electric vehicles or the fueling or charging infrastructure necessary for such vehicles. Includes measures to finance the acquisition or use of such vehicles or their fueling infrastructure among energy efficiency, water conservation, or electricity demand management programs in which agencies are authorized and encouraged to participate.