But the Islamist leader looked increasingly isolated, with ministers resigning, the liberal opposition refusing to talk to him and the armed forces, backed by millions of protesters in the street, giving him until Wednesday to agree to share power.
Mursi's office said the president had not been consulted before the armed forces chief-of-staff set a 48-hour deadline for a power-sharing deal and would pursue his own plan for national reconciliation.
Newspapers across the political spectrum saw the military ultimatum as a turning point.
"Last 48 hours of Muslim Brotherhood rule," the opposition daily El Watan declared. "Egypt awaits the army," said the state-owned El Akhbar.
The president's office said Mursi was meeting chief-of-staff General Abdel Fateh al-Sisi and Prime Minister Hisham Kandil for the second straight day.
The confrontation has pushed the most populous Arab nation closer to the brink amid a deepening economic crisis two years after the overthrow of Hosni Mubarak, raising concern in Washington, Europe and neighbouring Israel.
Military sources said troops were preparing to deploy on the streets of Cairo and other cities if necessary to prevent clashes between rival political factions.
Protesters remained encamped overnight in Cairo's central Tahrir Square and protest leaders called for another mass rally later in the day, dubbed a "Tuesday of persistence", to try to force the president out.
Senior Muslim Brotherhood leaders branded the military ultimatum a "coup", backed by a threat that the generals will otherwise impose their own road map for the nation.
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