Mr. Obama and the Hollywood actors were joined by Harry Ettlinger, a member of the real-life group that served as the film's inspiration.
Written and directed by Clooney, "The Monuments Men" tells the story of a World War II platoon -- made up of historians, artists and teachers -- tasked with rescuing cultural artifacts and works of art seized by the Nazis in Germany.
The White House says cultural heritage preservation is a vital foreign policy tool and helps strengthen bilateral relationships.
The film has underperformed at the box office, grossing $55.5 million worldwide against a $70 million budget, according to Box Office Mojo. Reviews have been tepid.