In Alexandria, the country's second-largest city, protesters took part in four marches, agreeing only in their opposition to Morsi. One group called on the military to launch an anti-Morsi coup, while another chanted "No military, no Brothers, Egyptian people are in the square." Another urged nationwide civil disobedience to topple Morsi.
Demonstrators gathered in smaller cities as well.
Thousands of people participated in demonstrations in Port Said, site of recent violent clashes. Several state agencies suspended work this week because of protests.
Those gathered outside the government headquarters urged protesters to remain peaceful. They set up committees to police the crowds.
In Desouk, about 50 miles east of Alexandria, protesters gathered outside the City Council in the early evening, al-Masry al-Youm said. They marched to the building after Friday prayers and launched a sit-in.
Demonstrators also blockaded a major bridge.
In Tanta, the country's fifth-largest metropolitan area, 60 miles north of Cairo, hundreds of people attacked the headquarters of the Muslim Brotherhood's political arm, the Freedom and Justice Party. They ripped down party banners, setting them on fire.
Some in the group marched on to the court building, where they threw stones.