"The message we have to send to the Muslim world is we expect you to work with us to keep our people safe," Obama said during a taped interview with CBS's David Letterman in New York. "We expect their full cooperation because that's the only way the world works."
Protesters have attacked US embassies and burned American flags after an obscure California-made film triggered an attack on the US consulate in the Libyan city of Benghazi last week that killed US Ambassador Christopher Stevens and three other Americans.
Obama, who has ordered tightened security at US's installations, called the video "offensive" but said it was not an excuse for violence.