Police fired tear gas to break up brief clashes that erupted between Morsi loyalists and residents of a central Cairo neighbourhood, AFP correspondents reported.
The confrontations began when dozens of religious scholars affiliated with Morsi's Muslim Brotherhood entered the religious endowments ministry and were ordered out by police, a security official said.
The scholars were joined by more pro-Morsi protesters who damaged shop fronts. That further infuriated the residents, who pelted them with stones, leading to sporadic scuffles on several streets.
Loyalists of the deposed president have set up two huge Cairo protest camps and have held near daily demonstrations for his reinstatement since his overthrow by the military on July 3.
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The standoff with the army-backed interim government, which has threatened to disperse the protest camps where thousands of Islamists have been staying for more than a month, has sparked international fears of further bloodshed.
Clashes between pro- and anti-Morsi demonstrators and security forces have killed more than 250 people since the end of June.
Since police issued an ultimatum last week to end the protests, the Islamists have repeatedly called for new demonstrations.
Morsi's backers set as their rallying cry: "Together against the coup d'etat and the Zionists," in an appeal to nationalist sentiment after a deadly air strike on militants in Egypt's Sinai Peninsula, which the jihadists said was carried out by an Israeli drone.
Israeli media say the Jewish state has been cooperating closely with Egypt over the threat from Sinai militants.
Authorities have announced plans to clear the pro-Morsi protest camps from Cairo's Rabaa al-Adawiya and Nahda squares by "gradual steps."