The moves sparked outrage among Egyptians who saw them as counter to what their fledgling democracy was supposed to have been all about.
Mohamed Badie, the Brotherhood's spiritual leader, exhorted the thousands of people who packed the area around the Rabaa Adawiya mosque in Cairo to fight back.
"The coup is illegal and we will never accept its results," said Badie, whose title is supreme guide of the Muslim Brotherhood. "We sacrificed so dearly to reach this point, and we will never return to the past again."
Badie challenged the Egyptian army to "return to the arms of the nation."
The furor appeared to escalate during the day. By nightfall, a car was burning on the 6th of October Bridge, which commemorates the 1973 Arab-Israeli war, and leads to Tahrir Square, a focal point for anti-Morsy demonstrators.
In Haram, a neighborhood of Giza in greater Cairo, one person was killed and seven were injured when a group of armed men attacked a police station, a spokesman for the health ministry said.
At least 10 people were injured in clashes between supporters of Morsy and residents in the city of Damanhour, about 160 kilometers (100 miles) northwest of Cairo, Nile TV said.
State television showed pictures from Alexandria of security forces firing tear gas at pro-Morsy demonstrators.
Outside Cairo University, throngs of pro-Morsy demonstrators formed human chains while others participating in a sit-in shouted, "Police are thugs!"
Mohamed Ismail was among those protesting near the university when he said he heard gunfire and saw "thugs" appear.
They carried guns and knives, he told CNN.
"I saw scores of people falling from the gunshots," he said. "But I do not know how many people were killed and injured."
Gunshots and birdshot were used in the clashes between the two sides, the state-run Al-Ahram news agency reported.
Egypt's armed forces said they would guarantee the rights of protesters as long the protests resulted in neither violence nor destruction of property.
Dismantling the Brotherhood?
In a move likely to spark further unrest among Morsy supporters, Egyptian authorities arrested the Muslim Brotherhood's deputy supreme leader, Khairat el-Shater, and Salafi politician Hazem Salah Abu Ismail, on Friday in Cairo.
Abu Ismail was being held on allegations of inciting the killing of protesters in front of the Muslim Brotherhood headquarters in Cairo, according to a statement released by the prosecutor's office.
El-Shater, who was the Muslim Brotherhood's first presidential candidate before being replaced by eventual president Morsey, was being held in connection with accusations he incited the killing of protesters in recent days, state-run TV reported.
The detention of the two men, who are wildly popular among their followers, has raised fears it could spur more supporters into the streets.
Police, meanwhile, were seeking hundreds of other Brotherhood members, state media reported.
A spokesman for the Freedom and Justice Party said Thursday the coup had turned into "very, very questionable attempts by the military to dismantle the Brotherhood."
The Freedom and Justice Party chief, Saad el-Katatni, and the party deputy, Rashad Al-Bayoumi, who were arrested Thursday, had been released, Nile TV, said Friday.
The Tamarod, or "Rebellion," movement, which had sought Morsy's ouster, has nominated Mohamed ElBaradei, an opposition leader, to become prime minister.
ElBaradei, the former head of the International Atomic Energy Agency, described Morsy's ouster as a "correction of the uprising of 2011."
Other opposition leaders and protesters have objected to the use of "coup" to describe the military's removal of the elected president via non-democratic means.