Reciprocal Market Access Act of 2013 - Prohibits the President from agreeing to the reduction or elimination of the existing rate of duty on any product in order to carry out a trade agreement with a foreign country until the President certifies to Congress that: (1) the United States has obtained that country's reduction or elimination of tariff and nontariff barriers and policies and practices with respect to U.S. exports of any product that has the same physical characteristics and uses as the product for which the President seeks to modify its rate of duty, and (2) any violation of the trade agreement is immediately enforceable by withdrawal of the duty modification until the President certifies to Congress that the United States has obtained the country's reduction or elimination of the tariff or nontariff barrier or policy or practice.

Requires the withdrawal of such a modification in specified circumstances determined by the Interagency Trade Enforcement Center until the President makes such a certification to Congress.

Requires the U.S. International Trade Commission (USITC), with respect to any proposed trade agreement that seeks a modification that would reduce or eliminate an existing duty on any product in order to carry out a trade agreement with a foreign country, to investigate the possible market access opportunities for similar U.S. exports to that country if such barriers and policies are modified or eliminated.