Human rights groups condemned on Wednesday the use of "excessive" force by Egyptian security forces and called for an independent investigation into clashes outside an elite army unit that left more than 50 people dead.

In a joint statement, 15 leading Egyptian rights groups expressed their "strong condemnation of the excessive force used by army and security forces" against supporters of ousted president Mohamed Morsi who were protesting against his overthrow by the military.

"Responses to demonstrations must comply with international standards, even if demonstrations witness violence or the use of firearms," said the groups, which included the Egyptian Initiative for Personal Rights and the Cairo Institute for Human Rights Studies.

Morsi's Muslim Brotherhood charged that security forces "massacred" their supporters as they were praying at dawn on Monday, while the army said it was responding to an attack by "armed terrorists."

Amnesty International said it had evidence pointing to the "disproportionate" use of lethal force by Egyptian security forces, and called for them to be reined in to avoid "disaster".

The rights groups' criticism of the army comes two days after at least 51 people, most of them supporters of the ousted Islamist president Mohamed Morsi, died in clashes outside the Cairo headquarters of the elite Republican Guard.

"Despite claims by the military that protesters attacked first during clashes on Monday and that no women and children were injured, firsthand accounts collected by Amnesty International paint a very different picture," the group's deputy regional director Hassiba Hadj Sahraoui said.

"Even if some protesters used violence, the response was disproportionate and led to the loss of life and injury among peaceful protesters," she added.

The rights watchdog said visits to mortuaries, hospitals and scenes of violence in Cairo and Alexandria, and testimony gathered from survivors and relatives of the dead suggested "the use of disproportionate force by the security forces, including intentional lethal force".

"Many of those killed and injured had been shot in the head and upper body with shotgun pellets and live ammunition," Amnesty added.

It said that unless the security forces were reined in and clear orders given on the use of force, "we're looking at a recipe for disaster".

The Egyptian rights groups and Amnesty all called for an "independent investigation" into the violence.

The army's ouster of Egypt's first freely elected president last week, after massive protests calling for his ouster, has pushed the divided country into a vortex of violence.

Amnesty said at least 88 people have died in political violence since Friday, including three members of the security forces. Some 1,500 people have been wounded.