At least 51 people were killed in recent protests.
Nine other leading Islamists including Mr. Badie’s deputy, Mohammad Ezzat, were ordered to be arrested on the same charges, state television said.
Prosecutors said the 10 suspects were involved in “inciting and aiding” clashes between backers of ousted president Mohammad Morsi and soldiers outside the headquarters of the elite Republican Guard on Monday in eastern Cairo.
At least 51 people, including an army officer, were killed in the clashes, raising the prospect of wider street violence in Egypt.
The army last week removed Mr. Morsi – the country’s first democratically elected president – after millions of Egyptians took to the streets demanding his resignation and early presidential elections.
The Brotherhood, the political party from which Mr. Morsi hails, has called his ouster a “military coup” and vowed open-ended street protests until he is reinstated.
The U.S. has conveyed “strongly and clearly” to the Egyptian military that the treatment of anyone who is being arbitrarily arrested – whether Mr. Morsi or other members of the Muslim Brotherhood – “is of importance” to Washington, State Department spokeswoman Jen Psaki said.
The interim government must follow due process and respect the rule of law, Ms. Psaki said. She noted that the U.S. has conveyed to the military that if arbitrary arrests of Brotherhood members continue, the group will be unable to participate in the democratic process, which is “contradictory to the whole point of having an inclusive process.”
Mr. Morsi supporters were camping in large numbers in the eastern Cairo area of Rabaa al-Adaweya.
Brotherhood spokesman Gehad el-Hadad said the latest arrest warrants were “the same tactics of the old police state.”
“They are trying to dismantle the protest in Rabaa al-Adaweya by arresting the figures who mobilise people there,” he said. “When you have a corrupt judiciary and a criminal police force, they can fabricate a story that makes sense to the people and bend the law as they see fit.”
The Islamist group has turned down an offer by prime minister-designate Hazem Beblawy to join the new government, in protest against Morsi’s ouster.
“We do not recognise the legitimacy or legality of any bodies set up since the coup or their representatives,” Mr. el-Hadad said.
Mr. Beblawy, a liberal economist, has started work on forming the government, which state media said would be sworn in Saturday.
A former finance minister, Mr. Beblawy has reached out to the Brotherhood in an apparent bid to defuse political tensions before his government’s inauguration.
“It is necessary for everyone to sit at the table of dialogue to solve the current political differences and stop street violence and bloodshed,” he said.
Interim President, Adli Mansour, a top judge, has promised to scrap jail terms for media offences, meeting a long-running demand by the country’s journalists, state-run newspaper al-Ahram reported online.
“As a judge, my conscience does not allow me to imprison those who have a different view,” Mr. Adli was quoted as saying.
Mr. Adli holds legislative powers until a new parliament is elected.
Kuwait said it would offer Egypt an urgently needed aid package of $4 billion (N645 billion).
“This assistance is a gesture of solidarity from the Kuwaiti people towards their Egyptian brothers,” said Abdullah al-Mubarak, Kuwaiti minister of state for cabinet affairs.
Saudi Arabia and the United Arab Emirates on Tuesday pledged $5 billion (N807 billion) and $3 billion (N483) in respective aid packages to Egypt.
Most Gulf governments had strained links with Egypt while the Brotherhood was in power, accusing the Islamist group of seeking to destabilise their countries.
Separately, Egyptian authorities partially reopened the Rafah border crossing with the Palestinian Gaza Strip after a series of attacks.
People stranded on both sides of the border were allowed to move through the crossing following thorough searches, security officials said.
The crossing, closed last week following attacks in Egypt’s Sinai Peninsula, is open for “humanitarian considerations” on Wednesday and Thursday, the officials said.
The crossing is to close again on Friday.
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