The Health Ministry said the casualties occurred in Cairo, Alexandria and Giza where demonstrations were held to mark the anniversary of the 2011 overthrow of President Hosni Mubarak.
An unknown number of injuries occurred and about 300 people were arrested, Ahram Online said.
The clashes pitted supporters of the Muslim Brotherhood against a coalition known as the Revolution Front, which opposes both the Brotherhood and the military government.
The Muslim Brotherhood denied any role in the bombing of a police training center in a Cairo suburb. No one was injured, but the blast came a day after four bombs targeting Egyptian police killed four people and injured at least 80.
The New York Times said the insurgent group Ansar Beit al-Maqdis appeared to claim responsibility for the blasts in a video message released Friday before the first explosion.