The New York Times reported at least 30 people had been killed across the country by early Saturday, though it was not possible to accurately assess the full extent of casualties.
Military helicopters were in the sky over Cairo as pro- and anti-Morsi forces fought near Tahrir Square -- street fighting that persisted for hours before soldiers in armored personnel carriers broke it up, the Los Angeles Times reported.
Gunfire erupted outside the officers' club of the Presidential Guard where Morsi is believed to be detained, the BBC reported. Troops initially fired rounds into the air but then fired at the crowd, the BBC said.
The Muslim Brotherhood called for the protest against the ouster of Morsi, Ahram Online reported.
Pro-Morsi marches took place in Alexandria, Beheira and Minyain, among other cities.
The African Union suspended Egypt's membership Friday, saying in a post on its Twitter page it was reacting to "the overthrow of the democratically elected Egyptian president," Voice of America reported.
The AU Peace and Security Council said during a meeting in Addis Ababa, Ethiopia, it would it send a delegation to Egypt "to work toward restoring constitutional order."
Navi Pillay, the United Nations' high commissioner for human rights, urged all parties in Egypt to commit to respect for human rights and the rule of law.
She said the large protests that preceded Morsi's overthrow show the desire for fundamental rights.
"I hope that the rule of law and a system of government that respects the human rights of all Egyptians -- men and women -- can be quickly re-established," she said in a statement Friday. "The country has so far failed to seize the opportunity to respond to the aspirations of all its citizens and move toward a truly tolerant and inclusive society, based on human rights norms and the rule of law. A concerted effort is needed by all parties to establish sound political and legal institutions."
Muslim Brotherhood lawyer Mustafa el-Demeiry told Ahram Online Friday the group's leader, Mohamed Badie, learned a warrant was issued for his arrest and would surrender but wasn't sure to which authority.
Egypt's army said it would permit peaceful protests and Muslim Brotherhood supporters prepared to rally for the ousted Morsi.
"Peaceful protest and freedom of expression are rights guaranteed to everyone, which Egyptians have earned as one of the most important gains of their glorious revolution," the army said.
Demeiry told Ahram Online Saad el-Katatni, chairman of the Muslim Brotherhood's Freedom and Justice Party, and Mahdi Akef, the group's former leader, were being held in Tora Prison with Abdel Moneim Abdel-Maqsoud, a brotherhood lawyer arrested Friday after going to the prison to defend the two leaders.
Interim President Adly Mansour, the chief judge of Egypt's constitutional court, pledged to hold elections based on "the genuine people's will," the BBC reported.
Gehad al-Haddad, spokesman for the Muslim Brotherhood, of which Morsi is a member, said the organization would not work with the new regime.
"We are being headhunted all over the country," Haddad said. "We are holding a mass rally after Friday prayers to take all peaceful steps necessary to bring down this coup."
State prosecutors said Morsi, who was in military custody, would face an investigation starting next week into claims he had "insulted the presidency," the British newspaper The Guardian reported.
Morsi was ousted Wednesday after days of protests across the country that left at least 50 people dead. Demonstrators accused Morsi and the brotherhood of pursuing an Islamic agenda and not tackling the country's economic woes.
The army said it had to step in after Morsi "failed to meet the demands of the people."
Mohamed ElBaradei, an opposition leader who backed Morsi's removal, said the army's intervention was "a painful measure" but ultimately averted civil war.
"Mr. Morsi, unfortunately, undermined his own legitimacy," he told the BBC.
Mohamed Soudan, foreign relations secretary for the Muslim Brotherhood-affiliated Freedom and Justice Party, said the military's actions pushed Egypt "back to the dictatorship regime."
Islamic fringe groups threatened payback for Morsi's overthrow, CNN reported.
Police arrested four men Friday who allegedly planned a revenge attack, and confiscated arms and explosives, al-Ahram reported.
A human rights watchdog called for an official inquiry into deaths resulting from politically motivated violence in recent weeks.
"The available information indicates that both supporters and opponents of Morsi -- and possibly security forces as well -- were responsible for needless loss of life," said Joe Stork, deputy Middle East and North Africa director for Human Rights Watch.