While calling the video "crude and disgusting" and saying the U.S. government had nothing to do with it, Obama said such expression can't be banned in a free society.
"Americans have fought and died around the globe to protect the right of all people to express their views — even views that we disagree with," Obama said. "We do so not because we support hateful speech, but because our founders understood that without such protections, the capacity of each individual to express their own views, and practice their own faith, may be threatened."
In an otherwise somber speech, Obama drew some laughter from his audience with a self-reflective defense of free speech. "Here, in the United States, countless publications provoke offense," he said, and as president "I accept that people are going to call me awful things every day, and I will always defend their right to do so."
He warned that newly elected leaders in countries that were swept by the Arab Spring uprising are threatened by the same anger and extremism now aimed at the U.S.
"The impulse towards intolerance and violence may initially be focused on the West, but over time it cannot be contained," Obama said. "The same impulses toward extremism are used to justify war between Sunnis and Shia, between tribes and clans."
While saying the future must not belong to those who slander Islam, Obama said, "Those who condemn that slander must also condemn the hate we see when the image of Jesus Christ is desecrated, churches are destroyed, or the Holocaust is denied."
Obama restated his call that the regime of Syria's Bashar Assad "must come to an end."
Romney also touched on the violence in the Muslim world in his speech at the Clinton Global Initiative, repeating a line of attack against Obama that he's been using this week in campaign appearances.