In a defiant 2 a.m. statement, 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.
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.
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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.
The Brotherhood's political wing, the Freedom and Justice Party, called on supporters to stage mass counter-demonstrations to "defend constitutional legitimacy and express their refusal of any coup", raising fears of violence.
One FJP leader urged "free revolutionaries" who supported Mursi to prepare for martyrdom