WASHINGTON, Jan 16 (Reuters) - The U.S. Supreme Court on Tuesday declined to hear an antitrust challenge by Epic Games, maker of the popular video game "Fortnite," to the way Apple runs its lucrative App Store, handing the software company a setback in its lengthy legal battle against the iPhone maker.

The justices turned away Epic's appeal of a lower court's decision that Apple's App Store policies limiting how software is distributed and paid for do not violate federal antitrust laws. The justices also decided not to hear Apple's appeal of the same decision, which barred certain App Store rules. (Reporting by Andrew Chung; Editing by Will Dunham)