Thousands flocked to the square after the military-appointed cabinet offered its resignation.
Egypt's cabinet says it has resigned amid deadly clashes between police and protesters demanding political change that have killed 26 and prompted the ruling military to call for crisis talks.
The cabinet announced its resignation on the third day of protests that have triggered Egypt's worst crisis since president Hosni Mubarak was toppled in February.
Two people were killed early Tuesday in the Red Sea town of Ismailiya, medics said, bringing the toll of clashes since Saturday to 26.
"The government of Prime Minister Essam Sharaf has handed its resignation to the (ruling) Supreme Council of the Armed Forces," cabinet spokesman Mohammed Hegazy said in a statement Monday.
State television quoted a military source as saying the ruling military council had rejected the resignation, but Information Minister Osama Heikal told the official MENA news agency the matter had not yet been decided.
Sharaf's resignation, if accepted, threatens to derail parliamentary elections scheduled for November 28 - the first polls since Mubarak's downfall.
The Supreme Council of the Armed Forces (SCAF), which took power when Mubarak was ousted, "invited all the political and national forces for an emergency dialogue to look into the reasons behind the aggravation of the current crisis and ways to resolve it as quickly as possible," it said in a statement carried by MENA. I
t said it had asked the justice ministry to set up a committee to shed light on the violence, and called on "all forces and citizens to commit to (restoring) calm, and creating an atmosphere of stability with the goal of pursuing the political process".
Amnesty International charged that Egypt's military rulers had failed to live up to their promises and had even committed worse rights abuses than the Mubarak's regime.
Tens of thousands of people packed Cairo's iconic Tahrir Square on Monday night, after clashes continued for a third straight day between protesters and police in and around the square.
They greeted news of the cabinet's resignation with indifference, calling for the removal of the military rulers as clashes continued around the nearby interior ministry headquarters.
Riot police fired volleys of birdshot, rubber bullets and tear gas at demonstraters who used stones and petrol bombs. Other protesters formed a corrider through which the injured were ferried into waiting ambulances.
The United States said it was "deeply concerned" by the violence and White House spokesman Jay Carney said it was important that Egypt, a US ally, move toward democratic elections.
UN leader Ban Ki-moon called on the military council to "guarantee" civil liberties as he deplored the deaths in the clashes.
"The secretary general calls on the transitional authorities to guarantee the protection of human rights and civil liberties for all Egyptians, including the right to peaceful protest," UN spokesman Martin Nesirky said.
Political forces behind the uprising have called for a mass rally on Tuesday to demand that the army cede power to civilian rule.
The Coalition of Revolution Youth and the April 6 movement, among others, have called for the protest at 4pm (0100 AEDT Wednesday) in Tahrir Square, the epicentre of rallies that ousted Mubarak.
In a Facebook page for the rally, the groups called for the immediate resignation of Sharaf's cabinet and the formation of a "national salvation" government.
They also demanded a presidential election by April 2012 and a complete overhaul of the interior ministry.
As clashes erupted on Cairo's Tahrir square, fighting also broke out in the Mediterranean city of Alexandria, state television said.
Hundreds have been injured during the protests that have raged in Cairo, Alexandria, Ismailiya and the canal city of Suez.
Culture minister Emad Abu Ghazi earlier quit in protest at the government response to the demonstrations, he told MENA. Arab League chief Nabil al-Arabi called for calm and urged all political forces to press ahead with the democratic process.
He urged them "to work for calm and return to the political process and move forward with the process of democratic change based on the principles of freedom, dignity and social justice on which the January 25 revolution was founded."
In a statement, 140 diplomats from the foreign ministry and Egypt's missions abroad called for "an end to the violence and attacks by security forces against peaceful protesters."
