In Alexandria, at least 19 people were hurt in clashes between the two sides, al-Masry al-Youm reported. Morsi supporters attacked demonstrators outside the Leader Ibrahim Mosque.
Inside the mosque, a preacher called the anti-Morsi protesters a minority.
In Cairo, thousands of people joined a pro-Morsi demonstration outside the Rabaa al-Adaweya Mosque in Nasr City, Ahram Online said.
Morsi was in Brussels where he met with Herman Van Rompuy, president of the European Union.
In an English-language statement published in al-Ahram and released to reporters he said the protesters are "counter-revolutionary forces aiming at destroying the gains of the revolution."
He said he does not have the power to change the date of a referendum on the draft constitution to be held Saturday and the following Saturday.
Opponents contend the draft constitution restricts freedoms and gives Islamist parties too much political influence.
The deputy chief of the Muslim Brotherhood's Freedom and Justice Party, Essam al-Erian, warned Thursday thugs may infiltrate the demonstrations to try to incite rioting by assaulting peaceful protesters, al-Masry al-Youm reported.
"All throughout the transitional phase, the counter-revolution tried to flood the country with bloody chaos, and now after the opposition announced participation in the referendum by calling for a 'no' vote, we have to beware of the attempts of thugs to cause chaos on Friday, or to assault peaceful protesters," Erian said on his Facebook page. "Each gathering has to protect its demonstrators from these criminals."