The protesters took to the streets in marches against the military, culminating in Tahrir Square where thousands were celebrating the anniversary of the 1973 war with Israel and voicing support for the army, Ahram Online reported.
Al-Jazeera reported that police fired tear gas and shots into the air to disperse the crowds.
The Interior Ministry said 300 pro-Morsi supporters were arrested during the clashes.
Meanwhile, the publishers of an Egyptian political magazine said someone planted a bomb in their building near Cairo's Tahrir Square this weekend.
Security officers disarmed the remote-control device, which was found on a wall outside the office of Rosa El-Youssef, which Ahram Online said was a state-owned publication.
A spokesman for the magazine said security in the area around Tahrir Square had been extremely tight ahead of planned political rallies marking the anniversary of the 1973 Arab-Israeli war. Security forces had been sweeping the area with bomb-detecting dogs and equipment.
Ahram Online said Cairo and other Egyptian cities have been rocked by a series of bombings since the July ouster of President Mohamed Morsi.