To affirm the importance of the Taiwan Relations Act, to provide for the transfer of naval vessels to certain foreign countries, and for other purposes.

[AI summary unavailable — showing source text] Naval Vessels Transfer and Arms Export Control Amendments of 2013 - Authorizes the President to transfer on a grant basis to: (1) Mexico, the OLIVER HAZARD PERRY class guided missile frigates CURTS and MCCLUSKY; and (2) Thailand, the OLIVER HAZARD PERRY class guided missile frigates RENTZ and VANDEGRIFT. Authorizes the President to transfer on a sale basis the OLIVER HAZARD PERRY class guided missile frigates TAYLOR, GARY, CARR, and ELROD to the Taipei Economic and Cultural Representative Office of the United States (which is the Taiwan instrumentality designated pursuant to the Taiwan Relations Act). Authorizes the President, when transferring any vessel named in this Act, to ensure that the total number of vessels transferred to a country named in this Act does not exceed the total number authorized for transfer to that country. States that: (1) the value of such vessels transferred on a grant basis shall not be counted against the aggregate value of excess defense articles transferred to countries in any fiscal year under the Foreign Assistance Act of 1961; (2) transfer costs shall be charged to the recipient; and (3) the country to which a vessel is transferred shall have neces…