Anti-Gunrunning Act of 2003

Anti-Gunrunning Act of 2003 - Amends the Brady Handgun Violence Prevention Act to prohibit any licensed firearms importer, manufacturer, or dealer from selling, delivering, or transferring: (1) two or more handguns to any single person (other than a licensed importer, manufacturer, or dealer) during any 30-day period; or (2) a handgun knowing or having reasonable cause to believe that the transferee has already received one or more handguns within the previous 30 days. Prohibits an unlicensed individual from receiving more than one handgun within any 30-day period. Specifies exceptions.

Provides for imprisonment for up to five years (currently, one year) of a licensed dealer, importer, manufacturer, or collector knowingly making any false statement in connection with required firearms records.

Requires a licensee, within three days of receiving a request from a prospective transferee, to notify the national instant criminal background check system of any check conducted within the previous 30 days that did not result in the transfer of a handgun.