Clashes between supporters and opponents of Mohamed Morsi killed four people on Monday as the ousted Egyptian president's family vowed to sue the army over his ouster.

At least 28 people were also injured in the violence between the rival groups of demonstrators in Cairo and the nearby town of Qalyub, emergency services said.

The latest bloodshed came as Morsi's family said they planned to sue the military for having "kidnapped" the elected president, who has been in custody since the July 3 coup.

It came despite an appeal by the army-installed civilian caretaker government for demonstrators to show restraint after weeks of nationwide demonstrations and deadly violence in the Sinai Peninsula.

Shaimaa Mohamed Morsi, the toppled president's daughter, told a news conference that the family was planning to take legal action in Egypt and abroad.

"We are taking local and international legal measures against Abdel Fattah al-Sisi, the leader of the bloody military coup, and his putschist group," she said of the army chief.

She voiced dismay at "the silence of rights organisations and civil society over the crime of kidnapping the legitimate president," whose election in June last year was widely regarded as Egypt's first free vote for a leader.

The family held General Sisi responsible for Morsi's safety.

Morsi has been detained at an unknown location since his overthrow.

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

The United States and Germany have led international calls for Morsi's release.

On Monday, the European Union reiterated these calls, urging "the release of all political detainees, including Mohamed Morsi," but Egypt's interim authorities have rejected them, saying he is being held in a "safe place".

Supporters of Morsi, who was ousted after a single year of his mandate, have pressed demonstrations, holding marches and protests across the country since his fall.

Some have led to bloody clashes and on Monday security and medical sources reported at least four people dead and 28 wounded.

One was killed and 26 wounded near Cairo's Tahrir Square, epicentre of the 2011 uprising that ended three decades of autocratic rule by Hosni Mubarak.

Police arrested seven people by the nearby Qasr al-Nil bridge after the clashes, and found two shotguns on them, a security source told AFP.

Three more died in Qalyub, in the northern outskirts of the capital, and two others were wounded, a security source in the town said.

Large crowds of Morsi supporters had held protests calling for his reinstatement.

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

Chanting "Sisi killer," and anti-police slogans, demonstrators also hung pictures of the ousted president on the gates of the public prosecutor's office.

In a televised address later, caretaker president Adly Mansour called on Egyptians to build a country "without rancour".

"We want to open a new page in the book of the history of the nation without rancour, hatred or confrontation," he said.

His call came as fresh attacks by militants in the Sinai killed one civilian and wounded four soldiers, one of them an officer.

The civilian was killed when militants opened fire on an army checkpoint on the main highway between the North Sinai provincial capital El-Arish and the Gaza border at Rafah, security sources said.

Since Morsi's ouster, militants have ratcheted up attacks on security forces in the increasingly lawless peninsula, killing four security force personnel and two civilians on Sunday. (AFP)