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.