Deadly clashes between supporters and opponents of Mohamed Morsi left 13 people dead, as pressure grew on Egypt's new leaders to release the deposed Islamist president.

The clashes broke out on Monday and raged into Tuesday, leaving dozens wounded alongside the fatalities, after Morsi's family vowed to sue the military over his ouster.

The interior ministry warned Tuesday it would deal with any lawlessness "firmly and decisively" while urging "everyone of all affiliations to maintain peaceful expressions of opinion" following the latest bloodshed.

Nine people were killed early Tuesday when opponents of Morsi attacked his supporters who staged a sit-in near Cairo University, the health ministry said, raising an earlier toll figure.

Four other people died late Monday, bringing the toll to 13 dead from 24 hours of clashes.

In the Al-Nahda area near the university, at least 16 cars had been torched in the clashes, an AFP correspondent said.

Later eight police officers were injured, some seriously, along with a number of civilians in a grenade attack at the Dahqaliya police station in the north, security forces said.

Morsi's family told a news conference on Monday they would take legal action against the military for having "kidnapped" the elected president after he was deposed in a popularly backed coup on July 3.

Egypt's new leadership says Morsi is in a "safe" place for his own good.

A spokesman for caretaker president Adly Mansour insisted that "Egypt is not a second Syria and anyone who pushes in that direction is a traitor."

Calls for Morsi's release have also been issued by the United States, Germany, the United Nations and the European Union.

"It is now of utmost importance that Egypt embarks on a transition, allowing a transfer of power to a civilian-led and democratically elected government," EU foreign ministers said on Monday.

They listed demands, including "the release of all political detainees, including Mohamed Morsi" -- reiterating remarks EU foreign policy chief Catherine Ashton made last week in Cairo.

Senior aides held with Morsi have asked their families for prison clothes, signalling possible charges, relatives said.

Khaled El-Qazzaz, the former president's secretary for foreign relations, and top adviser Essam El-Haddad made the request in telephone conversations last Friday, asking for white clothes, their relatives told AFP.

Prisoners awaiting trials or verdicts in Egypt wear white clothes, which may be provided by family members.

Morsi's Muslim Brotherhood movement has also vowed to sustain protests until his release and reinstatement, refusing to recognise the interim government installed by the military ahead of new elections early next year.

Tuesday's violence came a day after Morsi's supporters marched on the US embassy, setting off a gunfight with opponents in the nearby Tahrir Square that killed one protester.

Later in Qalyub, north of Cairo, street battles killed three people, one of them run over by a train as he tried to escape the violence.

Faced with the deadly clashes, interim president Mansour appealed in a speech delivered late on Monday for a "new page in the book of the history of the nation, without rancour, hatred and confrontation".

But Morsi's detention, and subsequent arrests of senior Brotherhood leaders, have hardened his supporters against dealing with the new regime.

His daughter Shaimaa Mohamed Morsi told reporters on Monday that the family would sue army chief General Abdel Fattah al-Sisi and also take legal action outside Egypt.

Morsi's son Osama said the family had not heard from him since his overthrow. "None of us has had any contact with our father since the afternoon of the coup on July 3," he told reporters.

UN High Commissioner for Human Rights Navi Pillay summoned Egypt's ambassador to Geneva this month and wrote to the new authorities in Cairo demanding explanations over Morsi's arrest.

Members of the now-dissolved upper house of parliament, which had been dominated by Islamists, held a defiant meeting in Cairo's Rabaa al-Adawiya mosque.

Demonstrators have also hung pictures of the ousted president on the gates of the public prosecutor's office.

Although mostly peaceful, pro-Morsi protests have claimed more than 100 lives in all.

In the bloodiest single incident, at least 53 people, mostly Morsi supporters, were killed outside the Cairo headquarters of the Republican Guard on July 8.

The Brotherhood accuses the army of committing a "massacre," while the military says it was responding to a "terrorist" attack.