At least 13 people died in clashes Friday across Egypt as police dispersed thousands of protesters demanding the reinstatement of deposed Islamist president Mohamed Morsi, the health ministry said.

The protests came after an Islamist alliance that backs Morsi called for demonstrations ahead of a new hearing on Wednesday in a trial of the ousted president.

Police moved in swiftly to disperse the rallies, after warning they would not tolerate protests by Morsi's Muslim Brotherhood following its designation as a terrorist group last week.

Five were killed in Cairo and the rest in other cities, the ministry said, adding that at least 57 people were wounded.

The ministry did not say whether the dead were protesters, police or bystanders.

The interior ministry said 122 protesters were arrested.

Police fought street battles with rock-throwing protesters in several districts of Cairo.

Protesters in the capital set fire to a police vehicle with petrol bombs, a security official said, with state media saying residents extinguished the fires.

In the upscale neighbourhood of Maadi, police fired tear gas near a military hospital as protesters threw fireworks at them, an AFP reporter said.

Protesters also clashed with police on a road along the Nile River and inside the suburb.

The street was littered with rocks and burning wood as police vehicles sped up and down the road to disperse the protesters.

The demonstrators regrouped in a side street, facing off with riot police and chanting "They are the thugs!"

Some protesters threw stones.

In an eastern neighbourhood of the capital, police also fired tear gas at thousands of Morsi supporters who burnt tyres and threw fireworks at security forces, another AFP correspondent said.

Gunshots were also heard.

Chants against military rule

Protesters chanted "Down with military rule" and slogans against army chief Abdel Fattah al-Sissi, who led Morsi's ouster in July.

Cairo's main squares were sealed off by security forces with barbed wire and military vehicles.

They included Tahrir Square, as well as Rabaa al-Adawiya and Nahda squares, which were the sites of a bloody crackdown on Morsi's supporters in August.

State news agency MENA reported a number were wounded by birdshot in clashes in Alexandria and that Morsi supporters set fire to two civilian cars.

Since the Morsi's ouster, his supporters have staged near-daily protests calling for his reinstatement, particularly after Friday prayers.

But their numbers have dwindled amid a violent government crackdown.

More than 1,000 people, mostly Islamists, died in street clashes following his overthrow, and thousands have been imprisoned.

Friday's protests come as a pro-Morsi coalition spearheading the protest movement called for demonstrations ahead of the resumption of his trial on Wednesday.

Morsi is being tried on charges of inciting the killings of protesters during his presidency.

He will also stand trial on January 28 over a jailbreak during the 2011 popular uprising that toppled long-time ruler Hosni Mubarak.

And a date for him to be tried on espionage charges has yet to be fixed.

Egypt's military-installed government declared Morsi's Muslim Brotherhood a "terrorist organisation" last month after accusing it of a suicide car bombing at a police headquarters that killed 15 people.

The Brotherhood denied the accusation, and an Al-Qaeda-inspired group claimed responsibility for the bombing.

The designation carries harsh penalties for offenders, including possible death sentences for the movement's convicted leaders and five-year jail terms for protesters.

Promoting the Brotherhood either in writing or verbally can also lead to prison sentences.

"We are not afraid, we love Egypt and what we are doing is for Egypt," said protester Mohamed Dahi, 39, as he distributed leaflets calling for the boycott of a referendum on a new constitution to be held this month.

"I am against all injustice and the military rule. I won't accept any military rule in Egypt," he told AFP as he participated in a protest along with his 10-year-old son.