Eleven people were shot dead as supporters of the Muslim Brotherhood clashed with police across.
Islamists opposed to the army's overthrow of President Mohammed Mursi in July have been holding daily demonstrations,
The army-backed government declared the Muslim Brotherhood a terrorist group last week, increasing the penalties for dissent.
The government is using the new classification to detain hundreds of brotherhood supporters.
Thousands more, including top leaders of the group, have been in jail for months, arrested in the aftermath of the army takeover.
The crackdown has reduced but not entirely broken the ability of the brotherhood to mobilise protests.
It has lately been relying on students to sustain momentum against what it refers to as the "putschist regime" governing Egypt.
In the Cairo district of Nasr City riot police in bulletproof vests fired teargas at protesters throwing fireworks and stones.
Similar clashes erupted across the country, as has become commonplace after midday prayers each Friday, not a working day in Egypt.
The Health Ministry said three protesters were killed indifferent districts in Cairo.
A security source said they died from bullet wounds, though it was unclear if the police or armed civilians had shot them.
In a separate incident, showing the deepening divisions since Mr Mursi was ousted, a man yelling insults at pro-brotherhood demonstrators marching near his house was shot dead by the protesters, a security source said.
A male protester and a woman were shot dead in the coastal city of Alexandria, medical and security sources said.
It was not clear whether the woman was a protester or an onlooker.
Another demonstrator was shot dead by police in the Suez Canal city of Ismailia after a march set off from a mosque after midday prayers, medical sources said.
In the rural province of Fayoum, southwest of Cairo, three protesters, including a student, died from bullet wounds to the chest and head.
Another university student was shot dead during clashes in the southern town of Minya. The Health Ministry said 42 people were wounded nationwide.
Police arrested 122 Brotherhood members for possession of weapons, the Interior Ministry said in a statement.
The brotherhood says its supporters are unarmed.
About 350 police and soldiers have been killed in bombings and shootings since Mr Mursi was ousted.