The ultimatum, it said, was a "last chance."
It described the mass protests on Sunday that brought out millions of Egyptians demanding President Mohammed Morsi's ouster as "glorious." It said protesters expressed their opinion "in peaceful and civilized manner," and that "it is necessary that the people get a reply ... to their calls."
The military underlined it will "not be a party in politics or rule." But it said it has a responsibility to act because Egypt's national security is facing a "grave danger," according to the statement, read out on state television.
"The Armed Forces repeat its call for the people's demands to be met and give everyone 48 hours as a last chance to shoulder the burden of a historic moment for a nation that will not forgive or tolerate any party that is lax in shouldering its responsibility," it said.
It did not directly define "the people's demands," but said if they are not realized, the military is obliged to "announce a road-map for the future and the steps for overseeing its implementation, with participation of all patriotic and sincere parties and movements."
It is the second ultimatum to be given to Morsi and the opposition to reach an agreement. Last Sunday, Defense Minister Abdel-Fattah el-Sissi gave the two sides a week to reach an agreement. That ultimatum expired on Sunday, with Morsi repeating his longstanding offer for dialogue that the opposition rejected.
The organizers of Sunday's protests also gave Morsi a Tuesday 5 p.m. deadline to step down or face an escalation of the campaign to force him out, including civil disobedience.
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