Thousands of Morsi's supporters protested on Friday in the capital Cairo, the second biggest city of Alexandria and other coastal and Nile Delta towns, the security sources said.
"Clashes erupted in Alexandria between pro-Morsi protesters and residents who oppose Morsi," said one of the sources, who asked not to be identified.
Smaller clashes also broke out in the Nile Delta province of Sharqia and the coastal city of Damietta, where one Mursi supporter was injured.
On Aug. 14, Egyptian security forces broke up the two main pro-Morsi sit-ins in Cairo and killed hundreds of civilians.
The army-backed government then declared a state of emergency and imposed a curfew. Thousands of Brotherhood members, including Morsi himself, have been arrested.
Around 57 people were killed in clashes between Morsi's supporters and opponents last Sunday, one of the bloodiest days since the army seized power.
While the military intervention has the support of most Egyptians, the international community, and many Islamists in Egypt, have looked on with alarm as the army and police crack down hard on Morsi and his backers.
Egypt has been also fighting an Islamist insurgency in the largely lawless region, which is also near the Palestinian Gaza strip. Sinai-based militants have intensified their attacks on military and police units since Mursi's ouster.
Six soldiers were wounded on Friday when a bomb exploded near army vehicles in Rafah city, northern Sinai, according to state media. Around 150 security personnel have died in Sinai's insurgency since Morsi was toppled, according to an army source.
NJF/NJF