In Athens, six people were detained during the demonstration at a central square, police said. About 600 people attended the rally, which featured heated speeches, but was mostly peaceful.
The crowd then wanted to march to the U.S. Embassy, which is about two miles from Omonia Square. Some tried to break through police lines several times, but riot officers pushed them back.
The violence occurred at the end of the rally, when small groups of protesters threw objects at police. Three cars were damaged and three storefronts smashed.
Banners were displayed in English, denouncing the film and called on the United States to hang the filmmaker. One told President Obama "we are all with Osama," referring to Osama bin Laden, the al-Qaeda leader who was killed in a U.S. raid in Pakistan in May 2011.
The amateurish film, which portrays the prophet as a fraud, a womanizer, and a child molester, has sparked violent protests throughout the Muslim world for nearly two weeks. The violence linked to protests over the film has resulted in the deaths of at least 49 people, including the U.S. ambassador to Libya.
About 300 Iranian students protested against the caricatures that appeared in the French weekly. They rallied in front of the French Embassy in Tehran, burning French, U.S., and Israeli flags and chanting "death to France" and "down with the U.S." They called for the expulsion of the French ambassador.
In Bangladesh, schools and businesses were closed and transportation was disrupted across the south Asian country as hard-line Islamic groups protesting the film enforced a general strike. The strike was called in response to police action Saturday against supporters of the groups that rallied in the capital, Dhaka, to denounce the film.
About 300 Christians, Sikhs, Hindus, and Muslims peacefully rallied in Pakistan's capital, Islamabad, to protest the film.
"There will be no peace in the world until we respect each other's religion," Sikh leader Deedar Singh said.
The protesters marched just over a half mile on Islamabad's main avenue near the parliament building.
The flare-ups have had an effect on the U.S. presidential race. As the anti-American protests erupted this month, Republican Mitt Romney called the president's handling of the situation "disgraceful" and decried a lack of U.S. leadership in the region.
President Obama, in an interview that aired Sunday on CBS's 60 Minutes, defended his foreign policy record, and said that "If Gov. Romney is suggesting that we should start another war, he should say so."