Egyptian police fired tear gas to prevent opponents of President Mohammed Mursi storming a court and the prosecutor-general's office.
Eight people were injured in Cairo during another protest in al-Fayoum south of the capital.
Some 500 people marched for much of the day through central Cairo, chanting "The people want to topple the regime" on the fifth anniversary of the founding of the opposition April 6 youth movement.
When some protesters hurled fireworks and rockets at the court, which also houses the prosecutor's office.
They tried to break down the main gate, police fired tear gas from upstairs windows.
Egypt has been in political turmoil since the ousting of President Hosni Mubarak in 2011.
President Mursi and his Islamist allies pitted against various secular opposition groups.
The prosecutor-general angered activists a week ago by questioning a popular TV satirist.
The TV satirist is accused of having insulted Mr Mursi.
The government denies opposition claims that the case is evidence of a crackdown on dissent.
Separately, opponents and supporters of the Muslim Brotherhood, Mr Mursi's Islamist allies, attacked each other with stones and fireworks in the Mediterranean city of Alexandria.
Meanwhile, five Egyptians have been killed and eight people have been injured in clashes between Christians and Muslims in a town near Cairo.
Christian-Muslim confrontations have increased in Muslim-majority Egypt since the overthrow of former President Hosni Mubarak in 2011.
The change in government has given freer rein to hardline Islamists repressed under Mubarak's rule.
Four Christians and one Muslim were killed when members of both communities started shooting at each other in Khusus outside the Egyptian capital.
The violence broke out when a group of Christian children were drawing on a wall of a Muslim religious institute.
A local church was attacked during the clashes and parts of it set on fire.
Police had stepped up security at the church after Muslim youths began gathering in the area.
The town was quiet on Saturday with a heavy security presence, a security source said. Some 15 police cars were patrolling the streets.
15 people have been arrested.
President Mohammed Mursi, a Muslim Brotherhood leader elected in June, has promised to protect the rights of Coptic Christians, who make up about 10% p of Egypt's 83m people.
Since Mubarak was ousted by a popular uprising, Christians have complained of several attacks on churches by radical Islamists.
The incidents have sharpened longstanding Christian complaints about being sidelined in the workplace and in law.
As an example, they point to rules that make it harder to obtain official permission to build a church than a mosque.
Last month, a court sentenced a Muslim to death for killing two people in a dispute with Christians in a southern town.
