One person died in Damietta when a rally in support of ousted president Mohamed Morsi was attacked, Ahram Online reported. Dozens of people were reportedly injured in the attack.
A pro-Morsi supporter also was killed, and several other demonstrators injured, in the Sidi Gaber district of Alexandria.
The casualties occurred as Morsi supporters scuffled with local residents outside a mosque in Alexandria after noon prayers. The two groups threw stones back and forth at one another, Ahram Online said.
Two people were taken to a hospital, said Osama Abou El-Soud, the head of the main university hospital. One person had been stabbed in the chest, while the other was shot.
Some 23 Muslim Brotherhood protesters were arrested following the Alexandria disturbances.
The violence came one day after the National Alliance to Support Legitimacy, which is led by Morsi's Muslim Brotherhood, called for non-violent demonstrations to support Morsi's reinstatement after his ouster in July.
In a statement Thursday, the group said it "maintains peacefulness in all its events" and urged supporters not "to lose hope as time goes by ... and not to be dragged into violence."
The National Alliance to Support Legitimacy condemned Thursday's bomb attack directed at Interior Minister Mohamed Ibrahim, in which 21 people were injured.