United States-Cuba Trade Act of 2003

Amends the Internal Revenue Code to declare the denial of foreign tax credit inapplicable to Cuba (except that such requirement shall apply to countries that have been determined to repeatedly provide support for acts of international terrorism).

Permits: (1) installation and maintenance of telecommunications equipment and facilities in Cuba, including telecommunications services between the United States and Cuba; and (2) travel to and from Cuba by U.S. citizens or residents.

Requires the U.S. Postal Service to provide direct mail service to and from Cuba.

Urges the President to take all necessary steps to conduct negotiations with the Government of Cuba to: (1) settle claims of U.S. nationals against Cuba for the taking of property; and (2) secure protection of internationally recognized human rights.

Expresses the sense of Congress that: (1) the United States should promote democratic change and economic reform by normalizing trade relations with Cuba; and (2) upon the enactment of this Act, it will no longer be necessary for the United States to continue to use Article XXI of the General Agreement on Tariffs and Trade (GATT) 1994 with respect to Cuba, understanding that the President retains full authority to invoke Article XXI and comparable provisions in other Uruguay Round Agreements in the future in all appropriate circumstances.

Amends the Harmonized Tariff Schedule of the United States to extend nondiscriminatory treatment (normal trade relations) to the products of Cuba.

Prohibits the Secretary of the Treasury from limiting the amount of remittances to Cuba that any U.S. person may make. Declares that this prohibition does not prohibit the prosecution or conviction of any person committing a criminal offense relating to the laundering of money or engaging in monetary transactions in property derived from unlawful activities.