CAIRO (AFP) - Egypt's new leadership faced increased difficulties on Thursday in forming an interim government after it issued a warrant for the arrest of the leader of the Islamist movement backing ousted president Mohamed Mursi.

Mursi'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 Mursi, the Brotherhood is now in tatters, with much of its leadership detained, on the run or keeping a low profile following the Islamist president'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 Mursi partisans, judicial sources said.

Mursi himself is currently being held in a "safe place, for his safety," foreign ministry spokesman Badr Abdelatty told reporters on Wednesday, adding: "He is not charged with anything up till now," he 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 "terrorist elements" 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.

Witnesses had contested its account, saying that the girl was killed after soldiers opened fire on the car she was in when her father refused to stop at a checkpoint.

Thousands of Mursi supporters joined those camped out at the Rabaa al-Adawiya mosque in Cairo's Nasr City, vowing to leave only when Mursi, the country's first freely elected president, is reinstated.

"We are gathering here for Mursi. I voted for him and I want to know where he is," said protester Mohammed, 47.

"We will stay here either until the president's return or martyrdom," he said.