"The road map guarantees achieving the principal demand of the Egyptian people -- having early presidential elections through an interim period through which the constitution will be amended," he said. "So all of us build it together and agree on a democratic constitution, so we can guarantee our freedoms."
The Egyptian military dominated the country for six decades and took direct power for a year and a half after Mubarak's ouster. On Monday, after a previous demand that Morsy offer concessions to the opposition, it gave him 48 hours to order reforms.
As the hour of the ultimatum neared, Morsy offered to form an interim coalition government to oversee parliamentary elections and revise the constitution that was enacted in January.
"One of the mistakes I cannot accept -- as the president of all Egyptians -- is to side with one party over another, or to present the scene from one side only. To be fair, we need to listen to the voice of people in all squares," he said.
Shortly after the deadline, Morsy aide Essam El Haddad said in a Facebook posting that a coup was under way and warned that the generals risked bloodshed by moving against Morsy.
"In a democracy, there are simple consequences for the situation we see in Egypt: The president loses the next election or his party gets penalized in the upcoming parliamentary elections. Anything else is mob rule," he wrote.
But Naguib Abadeer, a member of the opposition Free Egyptians Party, said what was under way "is not by any means a military coup. This is a revolution."
Morsy lost his legitimacy in November, when he declared courts could not review his decrees and ousted the country's prosecutor-general, Abadeer said. And the Muslim Brotherhood "hijacked the vote of the people" by running on a religious platform, "so these were not democratic elections," he said.
Obama says U.S. reviewing aid
In Washington, President Barack Obama said the United States is "deeply concerned" by Morsy's removal and the suspension of the constitution.
Washington has supplied Egypt's military with tens of billions in support and equipment over more than 30 years, and under U.S. law, that support could be cut off after a coup -- a term his White House statement avoided.
"The United States does not support particular individuals or political parties, but we are committed to the democratic process and respect for the rule of law," Obama said.
He said he had ordered "the relevant departments and agencies" to study what American law would mean for U.S. aid and urged the generals to hand power back to an elected government 'as soon as possible."
In the wake of Morsy's ouster, U.N. Secretary-General Ban Ki-moon echoed Obama's call for an immediate return to civilian rule. He appealed for "calm, non-violence, dialogue and restraint."
Wednesday's events capped days of massive demonstrations for and against Morsy. The demonstrations were largely peaceful, but health officials said 23 people died in clashes overnight at Cairo University, Al-Ahram reported.
Anti-Morsy demonstrators have ransacked Muslim Brotherhood offices around Egypt in the past several days.
Obama called Morsy on Monday to urge him to take a less-rigid stance toward his opponents, telling his Egyptian counterpart "that democracy is about more than elections," a White House statement said. But the State Department denied that Obama had urged Morsy to call early elections, as a senior administration official had said Tuesday.
Morsy's opposition said it had collected more than 20 million signatures on a petition to remove him -- millions more than the number who voted Morsy into the presidency.
Tuesday night, Morsy had vowed that he would not comply with the ultimatum and demanded that the armed forces stand down, even "if the price of upholding this legitimacy is my own blood." But political analyst Hisham Kassem told CNN the speech was Morsy's "final bluff."
"He was trying to give the impression 'We are there in numbers, and we are going to retaliate, we are not going to allow this to happen.' However, with almost 24 hours since his message, it's clear his supporters will not dare challenge the crowds on the street," Kassem said.
And faced with the throngs that filled Cairo's Tahrir Square, "the military had to intervene. Otherwise this crowd was going to get Morsy from his palace."
CNN spells the deposed president's name with a 'y' in accordance with what his spokesman said is his personal preference, his own e-mail and the country's Foreign Ministry.