Muslim Brotherhood spokesman Gehad El-Haddad told CNN the ousted president, Mohamed Morsi, was under house arrest at the presidential Republican Guard headquarters in Cairo; the military has not commented on Morsi's whereabouts.
The former chairman of the Muslim Brotherhood, Mahdi Aakef, and his bodyguards were arrested Thursday in Cairo with four weapons in their possession, according to the state-run Middle East News Agency, which cited security sources.
And Muslim Brotherhood supreme leader Mohamed Badei and the former supreme leader Mohamed Mahdi Akef have been arrested, Egyptian state broadcaster Nile TV said Thursday.
Arrest warrants have been issued for Badei's deputy, Khairat el-Shater, and other Brotherhead leaders on charges of inciting the killing of peaceful protesters in front of Brotherhood headquarters in Cairo's Moqattam neighborhood.
Police are seeking another 300 members of the Muslim Brotherhood, the state-run newspaper Al-Ahram reported.
Morsi and eight other former government officials -- all Brotherhood members -- had been placed on a "no-fly" list and were to be charged with "insulting the judicial authorities and its men," state-run EgyNews 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, state-run Al-Ahram newspaper reported.
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 Morsi, 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.
The 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.
The coup divided the hundreds of thousands of people who had taken to the streets across Egypt in recent days to defend or criticize Morsi's government.
It also raised questions about what will happen to Morsi 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 Tamarrod movement that had sought Morsi's ouster was moving on. It said in a tweet that it had nominated Mohamed ElBaradei, an opposition leader, to become prime minister.
The conflicting views, the threat of more violence, possible divisions among the anti-Morsi 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 Morsi's ouster Wednesday night with horns, cheering, fireworks had thinned.
On Thursday, the atmosphere in Cairo's Tahrir Square was calm and celebratory. Crowds cheered as five military helicopters flew overhead. Women pushed baby strollers, children had their faces painted, music played and people danced.
Morsi, 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.
Following a decree last month by Morsi, Mansour had become head of the court just two days earlier.
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.
Morsi's approval ratings plummeted after his election in June 2012 as his government failed to keep order or revive Egypt's economy.
Morsi'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.
The army's move against Morsi 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 Morsi'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, Morsi 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.
ElBaradei, the former head of the International Atomic Energy Agency and a leading opposition figure, said the plans announced Wednesday by the military represented "a correction for the way of the revolution" that drove Mubarak from office.
But Abdoul Mawgoud Dardery, a former member of parliament allied with Morsi, criticized the military's decision to take matters into its hands.
"I don't know how can anyone with common sense support a military coup in a democracy," he said. Egyptians "will never recognize a coup d'etat."
Outside observers echoed that concern.
"Popular protests are the sign of a robust democracy. But the change in an elected government should be at the ballot box, not through mob violence," said Ed Husain, a senior fellow for Middle Eastern studies at the Council on Foreign Relations.
Across the Nile River from Tahrir Square, Morsi supporters chanted, "Down with military rule," and "The square has a million martyrs."
A pro-Morsi protester in Cairo predicted demonstrators would stay "until Mohamed Morsi is once again president of Egypt."
"We're not violent, but at the end of the day we want peaceful change of power," El-Haddad, the Muslim Brotherhood spokesman, told CNN's Anderson Cooper. "But if democracy gets derailed every time that way, what other option is the people left with?"
'The world is looking'
Morsi 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 Morsi's statement aired, Al Jazeera reported its Cairo studios had been raided during a live broadcast and its presenter, guests and producers arrested.
"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.
Despite the moves against the Brotherhood, the military suggested Thursday it would protect the movement's members. The military said it would not allow any attacks or intimidation against those who belong to an Islamic group, state-run Nile TV reported.
But 32 people were killed Wednesday in clashes in Egypt, officials told Nile TV. Hundreds more were reported to have been injured.
The sporadic violence at times pitted Morsi's supporters against the opposition and the military, raising fears of spiraling unrest.
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 Morsi'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 Morsi'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 situation has created an uncomfortable policy scenario for the United States, which champions democratic principles.
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 emphatic 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."