Morsi's Muslim Brotherhood has spurned an offer from interim premier Hazem al-Beblawi to join the new government, and called for a mass rally on Friday against what it called "a bloody military coup."

After a year in power through Morsi, the Brotherhood is now in tatters, with much of its leadership detained, on the run or keeping a low profile following Morsi’s overthrow last week in a popular military coup.

Police were searching for the Brotherhood's Supreme Guide, Mohamed Badie, after a warrant was issued for his arrest on Wednesday, in connection with deadly violence in Cairo.

Badie and other senior Brotherhood leaders are wanted on suspicion of inciting clashes an army building on Monday which killed 53 people, mostly Morsi supporters, judicial sources said.

Military and judicial sources have said the ousted leader may face charges eventually.

His overthrow by the military last week, after nationwide protests demanding his resignation, has plunged Egypt into a vortex of violence.

In the restive Sinai peninsula, gunmen opened fire on the car of a senior military commander leading to clashes between security forces and militant groups, which left one girl dead, the army said in a statement.

The army later withdrew the statement from its official Facebook page, without providing an explanation.