The crowd clashed with the police throughout the night outside the US embassy, where thousands of protesters had climbed the embassy walls on Tuesday night and tore down the American flag, replacing it with a black Islamic flag.
Stones were hurled as police fired tear gas to disperse protesters who were banging stones on metal to make noise.
The Health Ministry said 70 people were injured in the clashes and 23 people were detained, state media reported.
As the situation remained grim, particularly after the violence against the US consulate in Libya, President Mursi asked Egyptians to respect law and refrain from resorting to violence.
At the same time, the President, who is on a visit to Brussels, condemned the controversial film that has provoked demonstrations across the Middle East.
"We Egyptians reject any kind of assault or insult against our prophet... (But) it is our duty to protect our guests and visitors from abroad," Mursi said in remarks broadcast by state television.
"I call on everyone to take that into consideration, not to violate Egyptian law... Not to assault embassies," he added.
Mursi also condemned the attack on US's Benghazi consulate that claimed the lives of four Americans, including the Ambassador.
"We all know that killing innocent people goes against Islam. The freedom to express opinions and demonstrate... Are guaranteed but without attacks on private or public property, diplomatic missions or embassies," Mursi said.
Protesters outside the US embassy in Cairo chanted a mix of anti-police songs, commonly sung by football fans and the ultras, and religious slogans.
"I am here to defend the prophet and to protest the securitymen who are Muslims and yet preventing me from letting my voice be heard. Nothing has changed under Mursi. The revolution will prevail," said protester Abdallah al-Masry, 27, of the Movement of the Revolutionaries of the Egyptian Street.
The Muslim Brotherhood, meanwhile, called for peaceful protests tomorrow.