Mr Badie is accused of inciting the violence in Cairo on Monday in which more than 50 people were killed.

Many Brotherhood members are already in detention and warrants are said to have been been issued for hundreds more.

Meanwhile, a foreign ministry spokesman has said ousted President Mohammed Morsi is being held in a "safe place".

Badr Abdul Atti told reporters he did not know where the 61 year old was, but that he was being treated in a "very dignified manner".

"For his own safety and for the safety of the country, it is better to keep him in a safe place. Otherwise, the consequences will be dire," he added.

Mr Abdul Atti is reported to have denied that Mr Morsi was being detained at the Presidential Guard barracks in Cairo, as many believe.

The Brotherhood, to which he belongs, says his ousting by the military a week ago amounted to a coup.

Its supporters have since been staging protests outside the capital's Rabaa al-Adawiya mosque, not far from the barracks, demanding his release and reinstatement.

The movement's political wing, the Freedom and Justice Party (FJP), has said it will not accept an offer to join the cabinet being set up by interim Prime Minister Hazem al-Beblawi, a 76-year-old economist and former finance minister who was appointed on Tuesday.

The arrest warrants could scupper any attempts to persuade the Brotherhood to participate in the transitional political process.

'Remain peaceful'

Spokesman Gehad el-Haddad said the charges against Mr Badie, known as the General Guide, and other senior leaders, were "nothing more than an attempt by the police state to dismantle the Rabaa protest".

Prosecutors also said they had ordered 200 people - believed to be Brotherhood members - to be held in custody for at least 15 days pending further investigation into accusations of murder, incitement to violence, carrying unlicensed weapons and disrupting public order. Another 450 have been released on bail.

There were conflicting reports about what happened on Monday, with the interim authorities being accused of a cover-up.

The Brotherhood maintains that soldiers carried out a massacre of peaceful demonstrators, who had been taking part in dawn prayers outside the Presidential Guard barracks.

But the police and the military say they acted in self-defence, and had opened fire only after being attacked by armed assailants.

More than 50 Brotherhood supporters were killed, as well as a soldier and two policemen.

On Wednesday, 15 leading Egyptian human rights groups expressed their "strong condemnation of the excessive use of force" against Brotherhood supporters, and called for an independent investigation into Monday's violence.

The previous Friday, Mr Badie had appeared at a rally outside the mosque, telling the crowd: "We shall stay in the squares until we bring President Morsi back to power."

He said their protests would remain peaceful and called on the army not to "direct your arms against us".

The BBC's Jim Muir, in Cairo, says the protest now covers several square kilometres of the capital, and to clear it out forcibly would almost certainly involve further bloodshed.

There is a feeling among the protesters that they have returned to the situation they were in under former President Hosni Mubarak, when the movement was banned and its members hunted down, our correspondent adds.

The timetable for new elections, announced in a constitutional declaration by interim President Adly Mansour on Monday evening, laid out plans to set up a panel to amend the suspended constitution within 15 days.

The changes would then be put to a referendum - to be organised within four months - which would pave the way for parliamentary elections, possibly in early 2014.

Once the new parliament convenes, elections would be called to appoint a new president.

A spokesman for Mr Mansour said posts in the cabinet would be offered to the FJP, but senior party official Mohamed Kamal told the BBC: "We will never take part in any cabinet as long as Morsi is not back as a president."

The FJP's deputy chairman, Essam al-Erian, earlier said the constitutional declaration had been issued "by a man appointed by putschists". The text does make clear that Mr Mansour and his government draw their authority only from the commander of the armed forces, who deposed President Morsi.

The main liberal coalition, the National Salvation Front (NSF), expressed reservations about the decree, saying it was not consulted and that it "lacks significant clauses while others need change or removal".

The grassroots Tamarod protest movement, which organised the demonstrations that led to Mr Morsi's overthrow, said the decree gave too much power to Mr Mansour.

Meanwhile, Saudi Arabia, the United Arab Emirates and Kuwait - who are opponents of the Muslim Brotherhood - have promised Egypt's interim government $12bn (£8bn) in grants, loans, and gas and oil.