Protesters flooded streets in central Cairo and in the second city Alexandria, carrying pictures of the deposed leader and chanting against the military coup that ousted Morsi on July 3.
In the oasis town of Fayyum, south of Cairo, Morsi loyalists clashed with police who fired tear gas to disperse them, security officials told AFP.
The government has said it held off from breaking up the Islamists' protest camps in Cairo out of respect for the holy month of Ramadan, which ended on Wednesday night, and to give foreign mediators a chance to end the deadlock peacefully.
"The government wants to give the protesters, especially the reasonable ones among them, a chance to reconcile and heed the voice of reason," said prime minister Hazem el-Beblawi.
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But he warned, in a statement late yesterday, "that the situation is approaching the moment we would rather avoid".
The main pro-Morsi coalition, the Anti-Coup Alliance, called for the marches to set off from different Cairo mosques after Friday noon prayers.
Pro-Morsi protesters also took to the streets in the central Egyptian city of Assiut, the official MENA agency reported.
An uptick in attacks, such as the bombing of a police station in a Nile Delta city on July 24, may ensue as more radical Morsi supporters turn to militancy.
"Short of a political agreement, the most likely outcome is a prolonged stalemate, repeated clashes and a transitional process in many ways fundamentally detached from reality," the International Crisis Group watchdog said.
"Nor should one underestimate the risk that some Islamists, convinced that the democratic process will never make room for them, drift towards violence," it added.
"A truce for Eid," read the headline of the state newspaper Al-Gomhuria today, as the countdown began to the dispersal of the Cairo protest camps.