Violent clashes between protesters and security personnel occurred in Cairo's Tahrir Square, Ismailiya, Dagahlia and Sharqiya, al-Masry al-Youm reported.
Mohamed ElBaradei of the National Salvation Front said he would agree to engage in talks with President Mohamed Morsi and other political officials in efforts to end the violence, Ahram Online reported.
Earlier, ElBaradei and other opposition officials had refused the president's request to engage in dialogue.
Opposition groups say the solution to the violence sweeping the country is to form a national unity government and rewrite parts of the Constitution, al-Arabiya reported. Parliamentary Affairs Minister Omar Salem said he would choose articles of the newly ratified constitution for amendment by a committee appointed by Morsi, Ahram Online said
Morsi also instructed governors in Ismailiya, Port Said and Suez to ease or annul the state of emergency imposed Sunday.
More than 59 people have been killed in demonstrations that led Morsi to declare a state of emergency in the three cities and impose a night-time curfew in an attempt to halt the unrest, al-Arabiya said.
Violence erupted Friday in Cairo when people marked the second anniversary and the ouster of President Hosni Mubarak with mass demonstrations. Unrest spread throughout the country, with protesters calling for Morsi's ouster.
In Port Said, protesters took to the streets Saturday after an Egyptian court sentenced 21 of 73 defendants to death for killing 70 fans during a 2012 soccer riot.