The Supreme Council of the Armed Forces is a body of senior generals which has vowed to guide Egypt to greater democracy.
The military council is expected to quickly suspend both houses of parliament and rule with the civilian head of the Supreme Constitutional Court for a transitional period of just a few months.
A free and fair presidential election has been promised for September.
It has also promised to end the 30-year-old emergency law - long used to stifle dissent through detention without trial - as "the current circumstances end." (The emergency law has been effect since 1981, after Hosni Mubarak became president following his predecessor Anwar Sadat's assassination.)
Thursday afternoon was only the third time in Egypt's history that the council had met. The other meetings were during wars with Israel, said Paul Sullivan, an expert on the Egyptian military at the National Defense University in Washington.
WHO'S IN CHARGE
Field Marshal Mohamed Hussein Tantawi, 75, Mr. Mubarak's veteran Defence Minister
As chairman of the Supreme Council of the Armed Forces, Field Marshal Tantawi is the senior figure in Egypt's new military regime. After Mr. Mubarak relinquished power, Field Marshal Tantawi drove past the presidential palace Friday and saluted cheering crowds.
U.S. officials have characterized Field Marshal Tantawi as someone who is "aged and change-resistant" and uncomfortable with the U.S. focus on fighting terrorism, according to a 2008 State Department cable released by the WikiLeaks website.
Lieutenant-General Sami Hafez Enan, 63, chief of staff of the armed forces
Gen. Enan visited Tahrir Square on Thursday and told protesters that their demands would soon be met. He presided along with Field Marshal Tantawi over Friday's meeting of the Supreme Council of the Armed Forces.
At 63, Gen. Enan is a generation younger than Mr. Mubarak. He has spent extended periods in the United States and is closer to U.S. commanders than the oldest Egyptian military leaders, including Field Marshal Tantawi, who were trained by the Soviet Union.
THE RISKS THEY FACE
The new situation exposes the army to demands for a civilian transitional government that could challenge or dilute its own authority or launch investigations into corruption or human rights abuses.
Another danger, commented the Arabist blogger Issandr Amrani, is that the army could become a target of the protesters. "The army's key problem … is that they suck at communicating," Mr. Amrani said. "Their battle to retain public legitimacy may be lost because of bad PR and tone-deafness."