An estimated 5,000 people were in the square and surrounding streets, according to the Guardian.
GlobalPost's live coverage of the events in Tahrir Square from our correspondents on the ground
Several hundred protesters spent the night there, the BBC said, defying the police's attempts to remove them.
Solidarity rallies have also been reported in Alexandria and Suez.
The AP reported that the Egyptian army, and police have launched major assault to evict protesters from Cairo's Tahrir Square, via Twitter.
According to reports by GlobalPost correspondents in Cairo, military police are tearing down a banner that says 'the people want a civilian council'. Erin Cunningham reported that soldiers told protestors that they are following orders, and that they want to avoid confrontation.
By Sunday morning, two people had been killed and 766 injured nationwide, according to the Egyptian Interior Ministry.
Witnesses in the capital say the crowd repeatedly attempted to march from Tahrir Square to the Interior Ministry building, but were forced back by police firing tear gas, rubber bullets and birdshot pellets.
More from GlobalPost: Clashes erupt between protesters and police in Egypt's Tahrir Square (VIDEO)
GlobalPost's correspondents in Cairo described dramatic scenes. Gunfire continued throughout the night and intensified early Sunday, Jon Jensen said on Twitter:
Shotguns and tear gas in downtown Cairo at 6:30am. Protesters held their ground, still tossing rocks at police - 17 hour later.
He also described seeing a Molotov cocktail hit a riot troop's helmet, "burning his face and forcing a massive police retreat."
Meanwhile GlobalPost's Erin Cunningham said she saw women, children and teenagers among the crowd.
To judge from Ahram's account, the protesters appear to be establishing a semi-permanent camp:
Despite the pervasive smell of tear gas, activists continue to erect new tents in the square, where several makeshift field hospitals have already been set up. Doctors have requested medical supplies to treat the wounded, most of whom are suffering from suffocation and other injuries.
Motorcycles were hastily converted into field ambulances to transport the injured to the field hospitals, while activists have begun collecting donations of medical supplies, blankets and food.
Demonstrators are calling for Egypt's military council, which took over following the fall of former president Hosni Mubarak in February, to hand over power to civilians.
The Interior Ministry accused protesters of inciting tension before upcoming parliamentary elections. Prime Minister Essam Sharaf issued a statement urging protesters to clear the square:
"What is happening in Tahrir is very dangerous and threatens the course of the nation and the revolution."
Egypt is due to hold elections on November 28.