Filing Relief for Natural Disasters Act This bill authorizes the Internal Revenue Service to postpone federal tax filing deadlines upon the written request of a governor of a state in which an emergency or disaster has been declared. The bill also extends current mandatory extensions from 60 to 120 days. For purposes of this bill, a state includes the District of Columbia, the Commonwealth of Puerto Rico, the U.S. Virgin Islands, Guam, American Samoa, and the Commonwealth of the Northern Mariana Islands.