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 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 Morsi partisans, judicial sources said.
Morsi himself is currently being held in a "safe place, for his safety," foreign ministry spokesman Badr Abdelatty told reporters 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, telling AFP 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 Morsi supporters joined those camped out at the Rabaa al-Adawiya mosque in Cairo's Nasr City, vowing to leave only when Morsi, the country's first freely elected president, is reinstated.
"We are gathering here for Morsi. 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.
According to the health ministry, 53 people died and 480 were wounded in Monday's clashes in Cairo.
The public prosecutor pressed charges on Wednesday against 200 of the 650 people it detained during the violence.
The warrant for Badie's arrest will make it harder for Beblawi to reach out to the Islamists as he attempts to form an interim civilian administration.
The liberal former finance minister, who began talks on his cabinet line-up on Wednesday, is ready to offer the Brotherhood ministerial posts, the state-run MENA news agency quoted an aide as saying.
But the Islamists spurned the overture. "We do not deal with putschists. We reject all that comes from this coup," Brotherhood spokesman Tareq al-Morsi told AFP.
Last week Badie gave a fiery speech in which he vowed that Brotherhood activists would throng the streets in their millions until Morsi's presidency was restored.
Interim president Adly Mansour has set a timetable for elections by early next year, while appointing Beblawi as premier and Nobel Peace laureate Mohamed ElBaradei as vice president for foreign affairs.
Opponents and supporters of Morsi alike have criticised the interim charter issued by Mansour to replace the Islamist-drafted constitution, which he suspended, and steer a transition the army has itself acknowledged will be "difficult."
An official with one of the parties in the National Salvation Front (NSF), the main coalition formerly led by ElBaradei, criticised Mansour's 33-article declaration for according extensive powers to the interim president.
Many within the coalition are wary of repeating the mistakes of the last military-led transition, between Hosni Mubarak's ouster in 2011 and Morsi's election in June 2012.
Human rights groups condemned the use of "excessive" force against Brotherhood supporters on Monday, and called for an independent investigation.
The United States, which provides 1.5 billion dollars in mainly military aid to Egypt, said it was "cautiously encouraged" by the timetable proposed for a new presidential election.
Kuwait pledged 4 billion dollars in assistance to Egypt on Wednesday, bringing the combined total pledged by Gulf Arab states since the coup to 12 billion dollars.
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