In a statement read out on state television, the armed forces reiterated its "call that the demands of the people be met and gives (all parties) 48 hours, as a last chance, to take responsibility for the historic circumstances the country is going through."
"If the demands of the people are not met in this period... (the armed forces) will announce a future roadmap and measures to oversee its implementation," the statement said.
The statement comes a day after millions took to the street demanding that Morsi resigns.
"It's an ultimatum directed to the president of the republic. He has been given 48 hours to accept what the people want and there is only one demand and that is to hold early presidential elections," said Hassan Nafea, political science professor at Cairo University.
In Tahrir Square, anti-Morsi protesters erupted in joy after the army's statement.
"Come down Sisi, Morsi is not my president," the protesters chanted, urging the country's army chief, Abdel Fattah al-Sisi, to intervene.
An official from Morsi's Muslim Brotherhood said the powerful movement was "studying" the army's statement.
Egypt is deeply divided between Morsi's Islamist supporters and a broad-based opposition.
The army had given all parties one week to reconcile their differences.
"This week, there has been no sign of gestures or acts," the army said.
"Wasting more time will lead only to more division... which we have warned and continue to warn against."