Puerto Rico Interstate Commerce Improvement Act of 2013 - Amends federal shipping law to revise coastwise endorsement requirements for certain vessels that transport liquified natural gas or liquified petroleum gas to Puerto Rico from other U.S. ports.

Repeals authority to issue a certificate of documentation with a coastwise endorsement for a vessel to transport liquified natural gas or liquified petroleum gas to Puerto Rico from other ports in the United States, if the vessel: (1) is a foreign built vessel that was built before October 19, 1996; or (2) was documented before that date, even if it is placed under a foreign registry and subsequently redocumented for operation.

Exempts from coastwise endorsement requirements self-propelled vessels that transport bulk cargo, including liquified natural gas or liquified petroleum bulk cargo, to Puerto Rico from another U.S. port or from Puerto Rico to another U.S. port.