The area has been the scene of violent clashes between supporters and opponents of President Muhammad Morsi.
The fighting, which continued overnight on December 5-6, left at least five people killed and several hundred wounded.
The army has deployed tanks outside the presidential palace.
The violence pitted Morsi's supporters from the Muslim Brotherhood and hard-line Islamist groups against liberals, leftists, Christians, and others.
The standoff was sparked by Morsi's decrees last month that gave him far-reaching powers, and a controversial new draft constitution. Morsi has called a referendum on the new charter on December 15.
The standoff is the worst political crisis in Egypt since mass street protests ousted President Hosni Mubarak last year.
Muhammad ElBaradei, a prominent opposition figure and Nobel Peace Prize laureate, said Morsi's rule was "no different" than Mubarak's.
"'We hold President Morsi and his government completely responsible for the violence that is happening in Egypt today," ElBaradei said.
"What is happening at the presidential palace at the moment, the violence, without the protection of the country, is an announcement from the country [leadership] and from the president that they do not practice their responsibility toward the protection of the country."
Morsi is expected to address the crisis in a speech to the nation on December 6.
Reports said some demonstrators began to disperse peacefully as the deadline set by the army passed.
Earlier on December 6, Morsi's opponents had vowed to continue protests.
There were reports of violent clashes in other Egyptian cities as well.
The opposition wants the president to rescind his November 22 decrees expanding his powers and withdraw the draft constitution that it says was rushed through an assembly dominated by the president's Islamist allies.
On December 5, Amr Moussa, an opposition leader and former head of the Arab League, called on the Egyptian people to come together in support of democracy.
"Here, in your presence, we are speaking in one voice in defense of Egypt and the continuation of Egypt's revolution," Moussa said.
"Today, tomorrow, and for all time, the Egyptian voice should be raised high that we are for a new and democratic nation and not the status quo, or the division of the Egyptian people, or the imposition of an unacceptable constitution."
Egypt's vice president, Mahmud Mekky. said amendments to disputed articles in the constitution could be agreed with the opposition but that the December 15 referendum would go ahead as planned.
The United States, which gives Egypt $1.3 billion in military aid each year, has called for dialogue.