Badie and other senior Brotherhood leaders are wanted on suspicion of inciting Monday´s deadly violence outside the Republican Guard headquarters where Morsi supporters were demanding his reinstatement, judicial sources said.[break]
Morsi is currently being held in a "safe place, for his safety," foreign ministry spokesman Badr Abdelatty told reporters, adding: "He is not charged with anything up till now," he said.
The Islamist president´s 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.
It is the latest in a string of attacks in Sinai "targeting the army and the police in recent days with the aim of sowing chaos and harming the stability and national security of Egypt," the army said.
In Cairo, more than 50 people died in Monday´s violence, most of them Morsi supporters.
The Brotherhood says troops and police "massacred" its activists as they were performing dawn prayers, with women and children among the dead.
The army said it was responding to an attack by "armed terrorists".
Thousands of Morsi supporters joined those camped out at the Rabaa al-Adawiya mosque in Cairo´s Nasr City for a prayer in honour of those who died, and vowed to carry on protesting until Morsi 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.
The protesters later headed towards the Ittihadiya presidential palace.
According to the health ministry, 53 people died and 480 were wounded in Monday´s clashes. It denied the Brotherhood´s claim that there were women and children among the casualties.
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 makew it harder for prime minister-designate Hazem al-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.
On Friday, 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.
Following Monday´s bloodshed, the Brotherhood called for an "uprising".
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 the divided nation through a transition the army has itself acknowledged will be "difficult."
The Brotherhood had already rejected the charter as a decree enforced by "putchists", and cracks have now emerged in the loose coalition that backed Morsi´s overthrow.
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 new powers to the interim president.
"You would look like a hypocrite now. It makes it look as if you are not against dictatorship, just against a dictatorship that is not from your group," the official said.
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 in mainly military aid to Egypt, said it was "cautiously encouraged" by the timetable proposed for a new presidential election.
Kuwait pledged $4 billion in assistance to Egypt on Wednesday, bringing the combined total pledged by Gulf Arab states since the coup to $12 billion.
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