Extra security measures were put in place for Saturday and arrests were reported in Cairo and Alexandria.
Rival protests took place in Cairo, where police broke up the anti-government demonstrations, leaving at least 29 dead and 147 injured, Egyptian health ministry official Ahmed Kamal said to the BBC.
Hundreds have died in clashes since the Egyptian army ousted President Mohammed Morsi in July.
The situation has been especially dire for Christians in Egypt, with many killed and others forced to flee.
The majority of the people killed in the most recent clashes were killed in Cairo, two were killed in Minya and one women killed in Alexandria, according to the BBC.
Police also arrested 139 members of the Muslim Brotherhood in Cairo, according to a USA Today report citing Egyptian state news agency MENA.