President Barack Obama spoke with Morsy on Wednesday "to review the strategic partnership between the United States and Egypt, and our ongoing efforts to strengthen bilateral economic and security cooperation," the White House said in a statement early Thursday.
During the call, the statement said, Obama told Morsy that "he rejects efforts to denigrate Islam, but underscored that there is never any justification for violence against innocents and acts that endanger American personnel and facilities."
For his part, Morsy "expressed his condolences for the tragic loss of American life in Libya and emphasized that Egypt would honor its obligation to ensure the safety of American personnel," according to the White House statement.
Tuesday, police and Egyptian army personnel formed defensive lines around the U.S. Embassy to prevent demonstrators from advancing, but not before the protesters had affixed a black flag atop a ladder in the American compound.
The flag was adorned with white characters that read, "There is no God but Allah and Mohammed is his messenger," a phrase often used by Islamic radicals.
Warning shots were fired as a crowd gathered around the compound, although it was not clear who fired the shots. There were no reported casualties.
Four protesters were arrested and were being questioned for "going off track to what is accepted as peaceful protesting," said Mahmoud, the Interior Ministry spokesman.
The Cairo incident was not nearly as bad as the violence in neighboring Libya, where an attack on the U.S. Consulate in Benghazi killed four Americans, including Stevens. The Libya attack has been blamed on a pro-al Qaeda group, according to sources tracking militant groups in the region.
It was unclear if the two attacks were coordinated. Protesters in both countries were upset over an online film that depicts Islam as a fraudulent religion and the Prophet Mohammed as a womanizer, child molester and ruthless killer.
In his statement, Morsy called on Egyptian diplomats in Washington "to take legal action against those people who seek to ruin relationships and discussions between people and countries."
The incident comes amid a delicate period in the relationship between the United States and Egypt under Morsy, the country's first leader since the overthrow last year of longtime ruler Hosni Mubarak, a key Western ally.
Embassy officials issued a warning to Americans in Egypt, telling them to avoid the demonstrations.
Frenzied protesters could be seen Tuesday afternoon holding up bits of a shredded American flag to television camera crews while chanting anti-U.S. slogans.
"This is an expression of a feeling that is thought to be an insult," said Nizih El Naggary, a spokesman for the Egyptian Foreign Ministry. "But events like this are extremely deplorable. And we have to work to get things under control."
Egypt's Foreign Ministry pledged to protect embassies and warned of the protests' potentially debilitating effects on the Egyptian economy.
Several individuals claimed responsibility for organizing the demonstrations, including Salafist leader Wesam Abdel-Wareth, president of Egypt's conservative Hekma television channel.
Demonstrations elicited a mixture of reactions from the Egyptian street, where last year tens of thousands turned out in opposition to Mubarak.
"These protests are a bad image for Egypt," said Ahmed, a Cairo street vendor. "Of course I'm against insulting Islam, but it's the undereducated, poor people who are out here causing problems."
"All I want for Egypt is security and stability," he said. "And as you can see this isn't it."
CNN's Mohamed Fadel Fahmy and Ian Lee in Cairo, Caroline Faraj, Jomana Karadsheh, Matt Smith, Brian Walker, Elise Labott, Paul Cruickshank and Tracy Doueiry contributed to this report
