Jeremy Bowen reports from Cairo where the army formed a protective barrier around protesters
Barack Obama has urged Egyptian President Hosni Mubarak "to make the right decision" to end weeks of unrest, and reiterated a call for an orderly transition of power "that begins now".
However the US president stopped short of telling Mr Mubarak to step down immediately.
He spoke as huge crowds demonstrated across Egypt for an 11th day, demanding that Mr Mubarak resign.
But PM Ahmed Shafiq said it would not be practical for the president to go.
He told the BBC Mr Mubarak's declaration on Tuesday that he would not seek re-election in September was tantamount to him standing down.
"In effect, the president has stepped down already," Mr Shafiq said. "We need him during these nine months."
He separately told al-Arabiya TV that it was unlikely Mr Mubarak would hand over power to his new Vice-President, Omar Suleiman, because the president was needed "for legislative reasons".
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Barack Obama: "We want to see this moment of turmoil turn into a moment of opportunity"
Meanwhile, there were suggestions that the protesters would reduce their presence in central Cairo, holding big demonstrations only on Fridays, with smaller numbers there at other times.
'World is watching'
More than 100,000 people - including large numbers of women and children - gathered in Tahrir Square in the centre of Cairo on Friday for what was being called the "day of departure".
At noon, thousands paused for Friday prayers with one cleric declaring: "We want the head of the regime removed."
As the prayers finished, demonstrators renewed their chants of "Leave! Leave! Leave!", singing patriotic songs and waving flags.
Some people left as darkness fell, but thousands remained the square.
There were also demonstrations in Egypt's second city, Alexandria, and in the towns of Suez, Port Said, Rafah, Ismailiya, Zagazig, al-Mahalla al-Kubra, Aswan and Asyut.
In Washington Mr Obama told reporters: "The whole world is watching."
He said he had been encouraged by the restraint shown by both the authorities and the protesters after two days of clashes which have left eight people dead and more than 800 injured.
The UN believes more than 300 have died across Egypt since the protests began on 25 January, with about 4,000 hurt.
Mr Obama did not insist that Mr Mubarak step down immediately, but repeated his call for a "transition period that begins now".
"He needs to listen to what is voiced by the people and make a judgment about a pathway forward that is orderly, that is meaningful and serious," he said.
"The key question he should be asking himself is: how do I leave a legacy behind in which Egypt is able to get through this transformative period? My hope is he will end up making the right decision."
BBC North America editor Mark Mardell says Mr Obama went further than before in suggesting that the Egyptian president should go, but could not quite bring himself - no doubt for very good diplomatic reasons - to say the words.
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“Start Quote
We want a civil state, based on Islamic principles”
End Quote Issam al-Aryan Muslim Brotherhood
The Obama administration is relieved that Friday's huge protests did not turn nasty, because violence is the biggest threat to the change it wants, our correspondent says.
There were real nerves in Washington that the army would be forced to choose between their commander-in-chief and the people, he adds. Instead they remained neutral, keeping the rival groups of demonstrators apart.
Opposition talks
The opposition has so far refused to attend any talks on a future government unless President Mubarak steps down, while the government says protesters must go home for talks to be held.
A US official told the BBC a meeting could be held in the coming days, and that the US was urging the government to move ahead with the dialogue.
