The Egyptian army has set up barricades outside the presidential palace, after ordering protesters to leave the area.
It follows violent overnight clashes between supporters and opponents of President Mohammed Morsi that left five people dead and 644 injured.
Most protesters left the palace by the 15:00 (13:00 GMT) deadline, though some opposition activists remained.
Meanwhile, Egypt's top Islamic body has called on the president to suspend his decree claiming sweeping powers.
The Al-Azhar institution also demanded an unconditional dialogue between the president and his opponents.
The BBC's Jon Leyne in Cairo says this move by one of the most respected bodies in Sunni Islam has put President Morsi - who was largely brought to power by the powerful Islamist Muslim Brotherhood - under more pressure.
Mr Morsi is expected to address the nation on Thursday evening, although his statement appears to have been delayed.
The president adopted new powers in the decree on 22 November, and stripped the judiciary of any power to challenge his decisions.
Mr Morsi, who narrowly won Egypt's first free presidential election in June, says he will give up his new powers once a new constitution is ratified.
But there is also controversy over the proposed constitution. Critics say the draft was rushed through parliament without proper consultation and does not do enough to protect political and religious freedoms and the rights of women.
The government insists that a referendum on the draft constitution, drawn up by a body dominated by Morsi-supporting Islamists, will go ahead this month despite strong opposition.
Four of Mr Morsi's advisers resigned on Wednesday - three others did so last week and the official Mena news agency reported a further resignation on Thursday.
The UN's human rights chief, Navi Pillay has urged respect for the right to peaceful protest.
"The current government came to power on the back of similar protests and so should be particularly sensitive to the need to protect protesters' rights to freedom of expression and peaceful assembly," Reuters quoted her as saying.
Tanks and armoured troop carriers were deployed outside the presidential palace on Thursday morning following the overnight clashes between the pro-Morsi Muslim Brotherhood supporters and his mainly secular opponents.
The Brotherhood said all those who died were its supporters, but this has not been independently confirmed.
Following a meeting between the president and military commanders, the 13:00 GMT deadline to clear the area round the palace was set. A ban on all protests in the area has also been ordered.
Concrete blocks and barbed wire barricades have been erected.
But the commander of the Republican Guard, Maj Gen Mohammed Zaki, said the security forces "will not be a tool to crush protesters", telling Mena: "No force will be used against Egyptians."
The Muslim Brotherhood supporters left the square before the deadline, but a few dozen opposition supporters remained in place and their numbers increased as evening fell.
The scene was calm, however, and there was no sign of any attempt to breach the military's barriers.
The opposition has said it will continue to hold demonstrations.
"We had many injuries last night, and we are not going to have their blood wasted," said an unnamed member of the National Salvation Front, a recently formed group which has united some of the most prominent anti-Morsi figures.
If the president is to defuse this crisis he will surely have to call off the referendum on a new constitution and give up the new powers, says our correspondent.
This would be a huge climb down, but otherwise this country could just be headed into more crisis and conflict, he adds.