Ayatollah Ali Khamenei, Iran's supreme leader, said the U.S. government should bring to justice those behind a film that ridiculed Muslims and the Prophet Mohammed.
Khameini on Thursday called the making of the film a "criminal act," according to the state-run Islamic Republic News Agency (IRNA).
His comments came the same day university students protested outside the Swiss Embassy in Tehran, blaming the United States and Israel for the American-made film.
The Swiss Embassy represents U.S. interests in Iran.
Two members of the film's production staff who spoke to CNN denied initial media reports that the filmmaker was an Israeli Jew.
Students read a statement in support of protesters who stormed the U.S. Embassy in Cairo and the U.S. Consulate in Benghazi, Libya, as word of the film spread.
U.S. Ambassador to Libya Christopher Stevens and three other Americans were killed in the Benghazi attack.
The semi-official Fars news agency and IRNA said additional protests across Iran are planned for Friday afternoon after prayers.
U.S. Secretary of State Hillary Clinton said Thursday, "This video is disgusting and reprehensible."
But, she added, there was no justification in responding to it with violence.