The military's statement, read on state television, said ministers now in office have been asked to remain until a new government has been formed, the BBC reported. It also suggested Egypt's policy toward Israel will remain the same for the moment.
"The Arab Republic of Egypt is committed to all regional and international obligations and treaties," the statement said.
Crowds remained in Tahrir Square in Cairo celebrating President Hosni Mubarak's resignation as the statement was being read.
While the military did not set any dates for the formation of an interim government or elections, the statement promised a transition to a "free democratic state." It also asked Egyptians to obey the police, and urged police officers to remember their force has the slogan "at the service of the people."
After Mubarak announced he was ending his 30-year rule Friday, thousands of protesters in Cairo, Alexandria and other cities celebrated in public squares and set off fireworks.
Vice President Omar Suleiman said Defense Minister Mohamed Hussein Tantawi was in charge, effectively meaning the military was in control.
In 18 days of anti-government protests, the military notably kept a low profile, unlike 1952, when the monarchy of King Farouk was overturned in a coup.
Barricades in Tahrir Square were being taken down Saturday, The Daily Telegraph said. Sweepers cleaned the square but some protesters said they would remain until the Army instituted democracy reforms.
The public jubilation over the potential for democratic elections under military rule appeared to ignore the sentiment of the 75-year-old defense minister, who said on national television "May God help everybody."