Morsy's ouster is a "conspiracy against legitimacy" and "a military coup that wastes the will of the people and returns Egypt to tyranny," the Muslim Brotherhood said in a post on its official website.
The Muslim Brotherhood, which is the Islamist movement that propelled Morsy to the presidency, also said that "millions condemn the coup and support the elected president's legitimacy."
It also suggested that elements of the regime of former President Hosni Mubarak, who was ousted in 2011 after massive demonstrations, are behind what happened to Morsy.
"The former regime is returning at the cost of the blood of ... martyrs," the Brotherhood's post said.
[Updated at 4:18 p.m. ET, 10:18 p.m. in Egypt]
We want to bring you up to speed on what the opposition leaders have been saying in the past hour. Mohamed ElBaradei, one of those leaders, said in a televised address that the political road map outlined by the military "responds to the demands of the Egyptian people."
He said that the road map -- which includes allowing the head of the country's constitutional court to be Egypt's temporary president until a new constitution can be drawn up and new elections can be held -- "guarantees achieving the principle demand of the Egyptian people of having early presidential elections."
[Updated at 4:15 p.m. ET, 10:15 p.m. in Egypt]
Cairo's Tahrir Square is still rocking, reports CNN's Reza Sayah from near the square.
"It's just jubilation. They're just rocking - it's a party," Sayah said.
The square -- the site of 2011 demonstrations that helped oust then-President Hosni Mubarak -- has been the heart of demonstrations that have now helped prompt Morsy's ouster. Thousands are cheering in the square, watching fireworks go off overhead.
[Updated at 3:59 p.m. ET, 9:59 p.m. in Egypt]
Despite the Egyptian military's forced ouster of Morsy, a former Egyptian general, Sameh Seif El Yazal, argues to CNN that what happened today isn't a military coup. He says the military isn't going to rule the country and that the military "supported the will of the Egyptians."
El Yazal said he expects elections to take place in nine to 12 months.
To recap what Gen. Abdel-Fatah El-Sisi, Egypt's top military leader, said about an hour ago: Morsy is no longer the leader of the country, and the head of the country's constitutional court will serve as Egypt's temporary president until a new constitution can be drawn up and new elections can be held.
It's not clear where Morsy is, although he, or someone on his behalf, appears to be sending messages through Twitter, as noted below.
[Updated at 3:52 p.m. ET, 9:52 p.m. in Egypt]
Morsy appears to be taking to Twitter.
A post on the Egyptian presidency's official account, attributed to Morsy, says the military's move represents a "full coup categorically rejected by all the free men of our nation."
The account also "urges civilians and military members to uphold the law & the Constitution" and "not to accept that coup which turns #Egypt backwards." This was posted just moments after the country's top military officer announced his ouster.