Egypt's military authorities have reaffirmed the country's commitment to all its international treaties.
The announcement, which was read by a senior officer on state TV, implicitly confirms that the country's peace treaty with Israel will remain intact.
Israeli PM Benjamin Netanyahu welcomed the announcement, saying the treaty was a cornerstone of Middle East stability.
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.
US President 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 Arab Republic of Egypt is committed to all regional and international obligations and treaties," the military statement said.
Our correspondent says this should allay the concerns of the United States and Israel, where politicians are anxious that a change in leadership could jeopardise the 1979 peace treaty.
Mr Netanyahu responded: "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."
The military also said it had asked the current government to stay on until a new one was formed, which would "pave the way for an elected civil authority to build a free democratic state".
It gave no official timetable for the transition.
But 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.