Thousands of Egyptians still occupy central Tahrir Square in the Egyptian capital, a day after the resignation of President Hosni Mubarak.
People have been cleaning the square as the army removes some barricades, even though tanks remain deployed.
After some 30 years in power, Mr Mubarak was forced out by 18 days of protests, handing power to the high command of the armed forces.
The council has said it remains committed to Egypt's foreign treaties.
Correspondents say it will be seen as reassuring in Israel, which has a peace treaty with its largest Arab neighbour.
US President Barack Obama called Egypt an inspiration, but said it must now move to civilian and democratic rule.
He is sending Adm Mike Mullen, chairman of the US joint chiefs of staff, to Jordan and Israel to discuss the impact of the changes in Egypt.
Shortly before the announcement of his resignation, Mr Mubarak left Cairo for the Red Sea resort of Sharm el-Sheikh, where he has a residence.
The anti-government protests that began on 25 January were triggered by widespread unrest in Egypt over unemployment, poverty and corruption.
Officials from Mr Mubarak's regime have now been banned from leaving the country.
Brooms and brushes
As dawn broke, Egyptians in Tahrir Square - the focal point of the protests - were still dancing, chanting slogans and singing songs.
But the army began removing some barricades to open one of the entrances of the square to traffic. And not long afterwards, as protesters began packing up the belongings of their makeshift camp, hundreds of people started streaming in, some carrying brooms and brushes - to begin a clean-up.
The square which a couple of weeks ago stank of riot gas, now reeks of disinfectant, says the BBC's From Paul Danahar.
Burnt-out vehicles were towed away as activists swept the streets and moved the rubbish away.
Others were listening to speeches from a stage on the east side.
"We have to stay," said one speaker, "until the army has given a contract to us to hand over power."
Outside the state TV building and government offices, the army and their tanks are still out in force.
So far the military have given few details of how they are going to run the country - it is not even clear if the vice-president or any of Hosni Mubarak's officials still retain their posts, says the BBC's Jon Leyne in Cairo.
The army have managed to give the impression of being above politics, a unifying force for the nation. But the opposition will want an early and clear indication that this country is headed in a new direction and not simply swapping one dictatorship for another, says our correspondent.
Announcing Mr Mubarak's resignation on Friday, Vice-President Omar Suleiman said the president had handed power to the army.
Mr Suleiman said on state TV that the high command of the armed forces had taken over, a body composed of high-ranking generals and headed by Defence Minister Mohamed Hussein Tantawi.
US diplomatic cables published by Wikileaks described Field Marshal Tantawi as "aged and change-resistant", but committed to avoiding another war with Israel.
In Tahrir Square the news was greeted with jubilation by a crowd of tens of thousands.
All over the city, drivers honked their horns and people fired guns into the air.
"We are a great people and we did something great. This is the expected end for every dictator," Mahmoud Elhetta, a protester, shouted.
The celebrations continued in other cities, with hundreds of protesters in Alexandria waving flags, whistling and dancing.
President Obama described the Egyptian people as an inspiration to the world for carrying out a non-violent revolution, adding: "Egypt will never be the same again."
Adm Mullen is visiting Israel and Jordan on Sunday and Monday.
"He will discuss security issues of mutual concern and reassure both these key partners of the US military's commitment to that partnership," Pentagon spokesman John Kirby said.
The BBC's Mark Mardell in Washington says that Egypt is a vital ally of America in the region and some are nervous about what change will mean.
Mr Mubarak's departure was greeted with jubilation throughout the Middle East and North Africa, including in Tunisia, where people overthrew their own president last month.
But Arab leaders in the Middle East and beyond should not sleep easy after the Egyptian uprising, says the BBC's John Simpson in Cairo.