Egypt's military authorities have pledged to oversee a transition to civilian rule, a day after the resignation of President Hosni Mubarak.
In a statement read out on state TV, they said they had asked the current government to stay on until a new one was formed.
The military also reaffirmed the country's commitment to all its international treaties.
The United States and Israel have welcomed the military's moves.
US President Barack Obama said he "welcomed the historic change that has been made by the Egyptian people".
He also "welcomed the Supreme Council of the Armed Forces' announcement today that it is committed to a democratic civilian transition, and will stand by Egypt's international obligations," a statement released by the White House said.
The announcement, which was read by a senior officer on state TV, implicitly confirms that the country's 1979 peace treaty with Israel will remain intact.
Israeli PM Benjamin Netanyahu also welcomed the announcement, saying the treaty was a cornerstone of Middle East stability.
"The longstanding peace treaty between Israel and Egypt has greatly contributed to both countries and is the cornerstone for peace and stability in the entire Middle East," he said.
Meanwhile the authorities have banned three senior officials close to Mr Mubarak from foreign travel.
The three are former Prime Minister Ahmed Nazif, former Interior Minister Habib al-Adli and current Information Minister Anas al-Fekky.
State TV said the men were under investigation, but no more details were available.
The moves came as thousands of people maintained a presence in Cairo's Tahrir Square, celebrating President Hosni Mubarak's resignation on Friday after 18 days of protests.
The BBC's Wyre Davis in central Cairo says there is still a huge party going on on the square, but a degree of normality is returning to other parts of the city.
The army has been encouraging people on the square to leave, he says, but its own presence there has been reduced, and there is a hardcore of protesters who want to stay until a full timetable of reform has been drawn up.
Our correspondent adds that a small army of volunteers and municipal workers have been clearing away debris from the streets.
In a number of US cities, emigre Egyptians held celebratory rallies on Saturday.
"Happy does not even describe it," said Ola Elsaid, now living near Detroit.
Ahmed Attidah, 30, of Chicago, said that for the first time he was considering moving back to Egypt.
"They need new minds and new blood. And going there, you would also be building a nation. That's exciting."
'Return to normal'
The military statement said the current government and regional governors would "act as caretakers of all businesses until a new government is formed".
It would look to guarantee "a peaceful transition of authority in a free democratic framework which allows an elected civilian authority to rule the country, to build a free democratic country".
"The Arab Republic of Egypt is committed to all regional and international obligations and treaties," the military statement added.
Later state media reported that Mohamed Hussein Tantawi, who heads the military high command which took power on Friday, had met Prime Minister Ahmed Shafiq and other senior officials to discuss "the immediate return of life to normality".
With Interior Minister Mahmoud Wagdy he discussed the rapid return to duty of the police, who left the streets in the early days of the protests, the media said.
The police force in Egypt was widely perceived as an instrument of repression under Mr Mubarak.
Protesters gave a cautious welcome to the army statement.
"It was a good thing," 21-year-old Muhammed Ibrahim told the Associated Press news agency. "We don't want there to be a political void."
Mr Mubarak, whose resignation was announced by his Vice-President, Omar Suleiman, on Friday afternoon, handed power to the high command, a body composed of high-ranking generals.
Shortly before the announcement, Mr Mubarak left Cairo for the Red Sea resort of Sharm el-Sheikh, where he has a residence.
The military has managed to give the impression of being above politics, a unifying force for the nation, says the BBC's Jon Leyne in Cairo.
But the opposition wants an early and clear indication that this country is heading in a new direction and not simply swapping one dictatorship for another, says our correspondent.
In a separate development, the regulator of Egypt's stock market said trading would be put off for three more days, opening again on Wednesday.
The exchange was closed on 28 January, three days after the protests began.
The demonstrations were triggered by widespread unrest over unemployment, poverty and corruption.