At least 10 people have been killed in clashes between police and protesters in eastern Cairo, officials said.
One policeman was among the dead and dozens of protesters were also injured, health officials confirmed.
The clashes follow the death of an activist in a march in Cairo on Saturday.
The protests were staged to mark the fourth anniversary of Egypt’s 2011 uprising, which toppled long-time leader Hosni Mubarak.
Security in major cities was tightened ahead of the anniversary, and key locations in Cairo were blocked off.
Dozens of people were killed in similar protests last year.
The police officer was killed during protests in Cairo, the interior ministry said, while protesters were killed in Cairo and the northern city of Alexandria.
Police said two militants were also killed as they tried to plant an explosive device in the Nile Delta.
On Saturday, activist Shaimaa al-Sabbagh was shot dead during a march by the socialist Popular Alliance party in central Cairo.
The party blamed police for her death. She was buried amid angry scenes in the northern city of Alexandria on Sunday.
Prosecutors have launched an investigation into her death.
Since ousting the elected president Mohammed Morsi in July 2013, the new Egyptian authorities have cracked down on political dissent.