The family of Egypt's ousted Islamist president said on Monday it would take legal action against the army as his supporters and opponents clashed in street battles in central Cairo.

Mohamed Mursi has been held at an undisclosed military facility since the army deposed him on July 3 and suspended the constitution in the wake of demonstrations against his one-year rule. The army says he is being held for his own safety.

His detention and the arrests of numerous senior members of his Muslim Brotherhood have fuelled fears of a broad crackdown against a group banned during Hosni Mubarak's 30 years of autocratic rule, until he was toppled by protests in 2011.

"There is no legal or constitutional basis ... for detaining someone not accused of a crime for his own safety," Mursi's son, Osama, told a news conference.

He said the family would take immediate legal action "inside Egypt and at an international level" against Abdel Fattah al-Sisi, the army commander and defence minister who played a central role in forcing Mursi from office.

The Muslim Brotherhood accuses the army of orchestrating a coup that has exposed deep fissures in the Arab world's most populous nation, a strategic hinge between the Middle East and North Africa.

White House spokesman Jay Carney called on Egypt to end "all politicised arrests and detentions", including the detention of Mursi. "We believe that his situation needs to be resolved in a way that is consistent with the rule of law and due process, and allows for his personal security," he told a briefing on Monday.

More than 100 people have died in violence since Egypt's first freely elected president was deposed.

On Monday, security forces fired tear gas to disperse hundreds of supporters and opponents of Mursi who hurled stones at each other near Cairo's Tahrir Square, centre of mass demonstrations before the fall of both Mubarak and Mursi.

State television said one person had died and seven were wounded in the worst violence in the capital since July 16, when seven were killed in confrontations.

"They're thugs, both sides," said Ahmed Sabri, an ice-cream vendor watching from a distance. "They don't speak for Egypt or Egyptians, they're just here for a fight."

"WILL OF THE PEOPLE"

In a brief television address on Monday, Egypt's interim president, Adli Mansour, said it was time for the country to turn a new leaf.

"No malice or hatred or division or clashes or tarnishing of those who gave. No breaking of those who worked hard. Now is the time to build our nation, reconciled with the past for a future that is reconciled with itself," he said.

The United States has so far avoided saying whether it regards Mursi's overthrow by the army as a "coup", language that could trigger the halt of $1.5 billion in mainly military US aid. But Western capitals have voiced concern about Mursi's fate and the European Union has called for his release.

The Brotherhood says it has had no contact with Mursi since he was overthrown, and that it believes he has not had access to a lawyer. Osama said the family had also not been able to contact him and had no information on the state of his health or where he was being held.

He described Mursi's removal as "nothing less than the abduction of the will of the people and the entire nation".

Mursi's supporters are maintaining a round-the-clock vigil in a Cairo suburb, now in its third week. They say they will stay put until Mursi is returned to office.

The military has installed an interim cabinet and promised a new election under a constitution now being amended to replace one drafted last year by a body dominated by Islamists and approved despite objections from Christians and liberals.

Egypt's public prosecutor's office launched a criminal investigation against Mursi on July 13, saying it was examining complaints including spying and inciting violence. It did not specify who had filed the complaints.

No formal charges have been announced and army and judicial sources denied on Monday a report in state-run Al-Ahram newspaper that the public prosecutor had ordered the arrest of Mursi for 15 days pending the results of a probe.

The prosecutor's office later summoned the newspaper's editor-in-chief to investigate what it called a "false report".

Heba Morayef, Egypt director of Human Rights Watch, said that without a detention order from the prosecutor's office, it was "completely illegal" to hold Mursi without charge beyond a maximum 48 hours. - Reuters