Heavy gunfire and explosions were heard in the centre of Cairo and tear gas was used. The government denied reports that a protester was killed.
Troops were out in force to prevent the protesters reaching Tahrir Square.
State TV reported further clashes in the northern Sharqiya district and to the east in Giza, as well as in the northern port city of Alexandria.
There were also reports of clashes between pro-Morsi demonstrators and civilian supporters of the military government.
One demonstrator was killed in the centre of the capital, according to some reports, although state TV carried a statement from the health ministry denying anyone had died.
Hundreds of Islamist protesters have died in violence since the Egyptian military deposed Mohamed Morsi in July.
Thousands of members of the Muslim Brotherhood have also been detained over the past two months.
Several senior figures, including Mohamed Morsi and the movement’s general guide Mohammed Badie, are being held on charges such as incitement to violence and murder.
The authorities portray the crackdown as a struggle against “terrorism”.
Protesters in the capital’s Agouza district were chanting “Rabaa, Rabaa”, a reference to the square next to the Rabaa al-Adawiya mosque where a sit-in was cleared by force in August.
Later, security forces fired tear gas at Morsi supporters as they tried to march towards Tahrir Square, the focus of the mass protests against Mohamed Morsi and his predecessor, Hosni Mubarak.
Troops also took up positions on both sides of Qasr al-Nil Bridge, which leads to the square from the Zamalek district.
Before Friday’s clashes, soldiers and police had tightened security around key sites in Cairo, including Tahrir Square.
Mohamed Morsi supporters have said they will be intensifying their demonstrations in the lead-up to Sunday’s 40th anniversary of the 1973 Arab-Israeli war.
Opponents who back the army have also said they will take to the streets.
In a statement issued on Thursday, the Brotherhood sharply criticized the officers behind the overthrow of Mohamed Morsi, comparing them to Adolf Hitler, the Roman emperor Nero and the Mongol conqueror Hulagu Khan.
It urged Egyptian soldiers to rebel and said it hoped that Sunday would mark a “victory by the people over those who staged a coup against them for personal gain”.
On Thursday, the European Union’s foreign policy chief, Baroness Catherine Ashton, held talks with armed forces chief General Abdul Fattah al-Sisi and interim President Adly Mansour, as well as with religious leaders.
“I got a real sense of everyone really trying to go forward in the right way,” she told reporters afterwards.
The previous day, a 16-year-old boy was killed in clashes between Mohamed Morsi supporters and opponents in the Red Sea city of Suez.
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