In the province of Fayoum, south of the capital, violence erupted after Morsi supporters staged a protest following Friday prayers, leading to the death of a 19-year-old student.
Security officials said police used tear gas after protesters fired birdshot at them.
The exact cause of the student’s death was not immediately clear, said health ministry official Medhat Shukri. He added that three policemen were also wounded in the clashes.
Another person was killed when pro-Morsi protesters clashed in the Ain Shams district northeast of Cairo with residents opposed to the Islamist president, who was toppled by the army last year.
Two other people were wounded in the clashes which erupted after the protesters fired birdshot and live rounds at Ain Shams residents, a Cairo police official said.
Security officials said that 13 people who took part in protests Friday in support of Morsi were arrested, including five in Fayoum who were found in possession of petrol bombs.
Supporters of Morsi still attempt to stage protests demanding his reinstatement, but their rallies have dwindled amid a deadly government crackdown since the army ousted the Islamist last year.
At least 1,400 people have been killed in the crackdown, while more than 15,000 have been jailed and hundreds sentenced to death.
The authorities have tightened security around universities after more than a dozen students were killed in violence sparked by pro-Morsi protests during the last academic year.-AFP