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Cairo, Egypt (CNN) -- Egypt's top prosecutor opened an investigation Thursday into claims that Mohamed Morsy and top leaders of the Muslim Brotherhood incited violence and the killing of protesters, a day after the military ousted the country's first democratically elected president.

The prosecutor, Gen. Abdel Maquid Mahmoud, issued an order preventing Morsy and 35 others from leaving the country while they are under investigation, state-run Middle East News Agency and EgyNews reported.

The news came as the Muslim Brotherhood and others called for Morsy supporters to take to the streets Friday across Egypt to protest the military's actions, while Egypt's armed forces announced it would guarantee the rights of people to protest as long it did not result in violence or destruction of property.

Even so, the military moved to arrest leaders of the Muslim Brotherhood who supported Morsy's rule and to silence their communications outlets.

Muslim Brotherhood spokesman Gehad El-Haddad told CNN that Morsy was initially under house arrest at the presidential Republican Guard headquarters in Cairo and later moved to the Ministry of Defense; the military has not commented on Morsy's whereabouts.

The news from MENA and EgyNews appear to contradict reports that Morsy refused an offer by the armed forces to leave Egypt for Qatar, Turkey or Yemen. The state-run newspaper Al-Ahram reported Thursday that Morsy would not step down voluntarily and that his speech Wednesday -- shortly before his ouster -- represented a "flagrant challenge to (the military's) authority" and a "declaration of confrontation with it."

A spokesman for Morsy's Freedom and Justice Party said that what started as a military coup was "turning into something much more."

In an interview in Cairo, El-Haddad cited the arrests as "very, very questionable attempts by the military to dismantle the Brotherhood."

Though El-Haddad has had no direct communications with Morsy, sympathizers within the military were giving information to the Brotherhood, he said.

The former head of the Muslim Brotherhood, Mohamed Mahdi Akef, and his bodyguards were arrested Thursday in Cairo with four weapons in their possession, according to MENA, which cited security sources.

Also arrested was the Muslim Brotherhood's current leader Mohamed Badei, Egyptian state broadcaster Nile TV reported Thursday.

Badei was arrested for "incitement to murder," according to the arrest report cited by Al-Ahram.

Police are seeking another 300 members of the Muslim Brotherhood, Al-Ahram reported.

On Wednesday, police closed the studios of pro-Muslim Brotherhood television stations Misr 25, The People and al-Hafez and arrested some of the journalists, according to Al-Ahram.

Sporadic violence

The Egyptian military also called Thursday for calm and unity, saying Egyptian values "do not allow for gloating or revenge between different groups" or for the destruction of private and public property, according to a statement posted on the Facebook page of the Supreme Council of the Armed Forces.

Even so, sporadic violence at times pitted Morsy's supporters against the opposition and the military, raising fears of spiraling unrest.

More than 100 people were wounded and at least two people, believed to be children, were killed in clashes across the country on Thursday, according to state media.

Violence was reported at a pro-Morsy rally Thursday in the northern city of Zagazig, Nile TV reported, citing security officials.

An Egyptian soldier was killed and two were wounded when rockets were fired at a police station in Rafah, on the border between Egypt and Gaza, news agencies, including Reuters and AFP, reported early Friday.

Rocket-propelled grenades were also fired at army checkpoints near the El Arish International Airport in the Sinai, near the border with Gaza, the agencies reported.

It was not immediately known if the attacks were connected to the overthrow of Morsy.

On its website, the Muslim Brotherhood declared "our unequivocal rejection of the military coup against the elected president and the will of the nation and refuse to participate in any action with the authority that stole the power and dealt violently with peaceful demonstrators."

It added, "Mohamed Morsy, president of Egypt, stresses that the measures that were announced by the General Command of the Armed Forces represent a full-fledged military coup which is unacceptable by every free person."

It called on demonstrators to show restraint.

The moves against the organization came as an uncertain new political order began to take shape with the swearing in of an interim president as well as the constitution's suspension on Wednesday.

State-run Al-Ahram News reported that Egypt's stock market surged 7% in the first hours of trading Thursday to a near two-month high.

Coup divides Egypt

The coup divided the millions of people who had taken to the streets across Egypt in recent days to defend or criticize Morsy's government.

It also raised questions about what will happen to Morsy and his supporters, who insist he remains the country's legitimate leader; whether violence blamed for the deaths Wednesday of at least 32 people will spread; whether democracy has a chance in Egypt.

But the Tamarod movement that had sought Morsy's ouster was moving on. It said in a tweet that it had nominated Mohamed ElBaradei, an opposition leader, to become prime minister.

ElBaradei told CNN on Thursday that Morsy's ouster was not a coup but was instead a "correction of the uprising of 2011."

Another opposition figure, Egyptian Conference Party leader Amre Moussa, took a similar semantic stance. "This is not a coup; this is a revolution," the former presidential candidate told CNN's Jim Clancy.

Asked whether the Brotherhood arrests were necessary, he said they would be temporary. "There are certain security measures that should not stay but for the first couple of days, three, four days -- the new regime wants to ensure that discipline will take place."

Democratic processes had been "absent" under Morsy, said the former Arab League secretary-general, who lost last year in his bid for the presidency.

Asked whether he would run again, he said, "I have declared several times before that I do not intend to run for president next time. This is my determination as I am talking to you."

The conflicting views, the threat of more violence, possible divisions among the anti-Morsy coalition and Egypt's economic woes represent major obstacles to a smooth transition, said Hani Sabra, director of the Middle Eastern arm of the Eurasia Group, a U.S.-based political risk research and consulting firm. "I don't think that the military's so-called road map is actually going to move smoothly. I think there are a lot of challenges it faces."

The huge crowds that had celebrated Morsy's ouster Wednesday night with horns, cheering, fireworks had thinned hours later. On Thursday, the atmosphere in Cairo's Tahrir Square was calm and celebratory. Crowds cheered as military helicopters flew overhead. Women pushed baby strollers, children had their faces painted, music played and people danced.

Swearing in

Morsy, a Western-educated Islamist elected a year ago, "did not achieve the goals of the people" and failed to meet the generals' demands that he share power with his opposition, Egypt's top military officer, Gen. Abdel-Fatah El-Sisi, said Wednesday in a televised speech to the nation.

Adly Mansour, head of the country's Supreme Constitutional Court, was sworn in Thursday as interim president in Cairo.

At the ceremony, Mansour said the Egyptian people had given him the authority "to amend and correct" the revolution that toppled Hosni Mubarak in 2011.

Until new elections, to be held at an unspecified date, Mansour will have the power to issue constitutional declarations, El-Sisi said.

The Egyptian military has dominated the country for six decades and took direct power for a year and a half after Mubarak's ouster.

Morsy's approval ratings plummeted after his election in June 2012 as his government failed to keep order or revive Egypt's economy.

Morsy's opponents accused him of authoritarianism and forcing through a conservative agenda, and on Monday the military gave him 48 hours to order reforms.

As the deadline neared Wednesday, he offered to form an interim coalition government to oversee parliamentary elections and revise the constitution, which was enacted in January. But those actions failed to satisfy the generals.

Conflicting responses

The army's move against Morsy and the Muslim Brotherhood, the long-repressed political movement that propelled him to office, provoked wildly conflicting reactions.

In Tahrir Square, the epicenter of two Egyptian upheavals, a vast gathering of Morsy's opponents erupted in jubilation and fireworks at El-Sisi's announcement Wednesday night.

"The crowd walked up to the barricades and started banging on them using rocks, sticks and even bare hands," said Sultan Zaki Al-Saud in a CNN iReport. "It sounded like thunder as the hollow barricades rang with every blow."

During his time in office, Morsy had squared off against Egypt's judiciary, the media, the police and even artists.

Egyptians are frustrated with rampant crime and a struggling economy. Unemployment remains high, food prices are rising and there are frequently electricity cuts and long fuel lines.

'The world is looking'

Morsy had remained defiant.

"The world is looking at us today," he said Wednesday in a taped statement delivered to the Arabic satellite network Al Jazeera. "We by ourselves can bypass the obstacles. We, the sons of Egypt, the sons of this country -- this is the will of the people and cannot be canceled."

Shortly after Morsy's statement aired, Al Jazeera reported its Cairo studios had been raided during a live broadcast and 28 staff members arrested. Most were later released, it said.

On Thursday, Al Jazeera's acting chief, Mostefa Souag, demanded the immediate release of the Egyptian channel's managing director, Ayman Gaballah, and Al Jazeera Arabic broadcast engineer Ahmad Hasan.

"A return to Mubarak-era practices of mass arrests and politically motivated imprisonment of Muslim Brotherhood leaders will have the worst possible effect on Egypt's political future," said Human Rights Watch, the U.S.-based advocacy group.

Concerns of a backlash

Some observers warned of an extremist backlash.

"The major lesson that Islamists in the Middle East are likely to learn from this episode is that they will not be allowed to exercise power, no matter how many compromises they make in both the domestic and foreign policy arenas," said Mohammed Ayoob, Michigan State University professor emeritus of international relations.

"This is likely to push a substantial portion of mainstream Islamists into the arms of the extremists who reject democracy and ideological compromise," Ayoob wrote in a CNN.com opinion piece.

President Barack Obama said the United States was "deeply concerned" by Morsy's removal and the suspension of the constitution.

He called upon the military to hand over power to "a democratically elected civilian government" but did not say it needed to be Morsy's.

At least three high-level conversations took place between U.S. military officials and their Egyptian counterparts in the past week, Pentagon officials said Thursday.

The president's national security team that has been in touch with Egyptian officials and regional allies urged a "quick and responsible" return to a democratically elected government, the White House said Thursday.

Washington has supplied Egypt's military with tens of billions of dollars in support and equipment for more than 30 years. Under U.S. law, that support could be cut off after a coup.

Obama said he had ordered "the relevant departments and agencies" to study how the change in power would affect U.S. aid.

The German government was more blunt in its assessment.

"This is a heavy setback for democracy in Egypt," German Foreign Minister Guido Westerwelle said. "It is very urgent for Egypt to return to constitutional order as soon as possible."

CNN's Ben Wedeman reported from Cairo; Tom Watkins and Chelsea J. Carter wrote from Atlanta. CNN's Jethro Mullen, Reza Sayah, Becky Anderson, Mohammed Tawfeeq, Ivan Watson, Jill Dougherty, Dan Lothian, Amir Ahmed, Ali Younes, Schams Elwazer, Elise Labott, Ian Lee, Housam Ahmed and Salma Abdelaziz contributed to this report.