CAIRO — Stepping from the cloud of tear gas in front of the American Embassy here, Khaled Ali repeated the urgent question that he said justified last week’s violent protests at United States outposts around the Muslim world.

“We never insult any prophet — not Moses, not Jesus — so why can’t we demand that Muhammad be respected?” Mr. Ali, a 39-year-old textile worker said, holding up a handwritten sign in English that read “Shut Up America.” “Obama is the president, so he should have to apologize!”

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