There is a stand-off in Cairo's Tahrir Square as protesters who have camped there for 20 days thwart army efforts to clear the area.
Thousands more people have made their way to the square, the focal point of the uprising that led to President Hosni Mubarak's departure on Friday.
The army seems undecided on how to respond to the fresh influx, reports the BBC's Jon Leyne from the scene.
The military police chief has called for tents to be cleared from the area.
"We do not want any protesters to sit in the square after today," said Mohamed Ibrahim Moustafa Ali, the head of military police.
US President Obama earlier welcomed the new military leadership's pledge to work towards civilian rule.
It has reaffirmed Egypt's commitment to all its international treaties, and asked the current government to stay on until a new one was formed.
Tempers frayed on Sunday morning as protesters realised hundreds of policeman - who had become hugely unpopular for their violent attempts to suppress the uprising - had entered the square.
The police chanted: "It's a new Egypt, the people and the police are one," echoing a popular chant by the anti-Mubarak groups in support of the army during the height of the demonstrations.
The crowd chanted back: "Get out, get out!"
For a few minutes there was a tense stand-off as the two sides confronted each other, before the police march peeled away and left the square.
Although there were reports of scuffles between soldiers and die-hard protesters in the square on Sunday morning, our correspondent said the operation to clear the area had previously been conducted without provocation.
A hardcore of several hundred protesters had remained marooned on a traffic island in the heart of the square, saying they would not move until a full timetable of reform was drawn up.
Throughout the weekend, an army of volunteers and municipal workers has cleared away debris from the streets.
Meanwhile, it has emerged that 18 antiquities - including statues of King Tutankhamun - have been stolen from the Egyptian Museum during the unrest.
Earlier, Mr Obama welcomed the new military leadership's statement aired on state TV on Saturday, which 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.
Former British Prime Minister Tony Blair - and current Middle East envoy - has said Mr Mubarak's departure could be a "pivotal moment".
"I think the single most important thing now is to accept that this is a moment of huge opportunity, not just for Egypt," Mr Blair told the BBC.
"This is a moment when the Middle East could pivot and face towards change and modernisation and democracy and that would be a huge benefit for all of us.
'Return to normal'
Saturday's military statement said the current government and regional governors would "act as caretakers", looking 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".
Later state media reported that the high command's leader, Mohamed Hussein Tantawi, had discussed with Interior Minister Mahmoud Wagdy the rapid return to duty of the police, who left the streets in the early days of the protests, reports said.
The police force in Egypt was widely perceived as an instrument of repression under Mr Mubarak.
The military has managed to give the impression of being above politics, a unifying force for the nation, 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.
The demonstrations were triggered by widespread unrest over unemployment, poverty and corruption.
Meanwhile the authorities banned three senior officials close to Mr Mubarak - former Prime Minister Ahmed Nazif, former Interior Minister Habib al-Adli and current Information Minister Anas al-Fekky - from foreign travel, saying they were under investigation.
Mr Mubarak resigned on Friday after 18 days of protests, and was flown to his luxury residence in the Red Sea resort of Sharm el-Sheikh.
He handed power to the high command, a body composed of high-ranking generals.