An AFP reporter said 11 people died on Sunday and two people on Saturday, kicking off a violent countdown to the country's first elections since the end of Mubarak's 30-year-rule.
At least four had been shot dead on Sunday, he said.
Earlier Dr Mohammed Fatuh, who heads a field hospital in the square, confirmed to AFP that three more bodies had been brought in bearing bullet wounds.
Medics earlier reported four deaths, one from live fire and three from asphyxiation after tear gas was fired.
Police and troops seized the square only to be beaten back by protesters who retook it later, as had also happened on Saturday.
The situation remained fluid with ongoing clashes around Tahrir -- the symbolic heart of protests that toppled Mubarak in February.
An AFP reporter said late on Sunday that on one street protesters were throwing stones and petrol bombs at armoured personnel carriers and riot police.
He said military police had responded with mostly shotgun fire and rubber bullets. When there was steady fire some protesters began to run while others chanted "Hold fast! Hold fast!" and "We won't leave!"
There were heavy clashes on side streets leading to the interior ministry as protesters chanted "The people want to topple the field marshal" -- Hussein Tantawi, Mubarak's long-time defence minister who heads the ruling military.
Activists tweeted a video they said showed police dragging a corpse on the ground, in what appears to be Tahrir Square, and leaving it by a rubbish dump.
In the Mediterranean city of Alexandria, a funeral procession for one of the victims degenerated into clashes with the police who fired volleys of tear gas at mourners, the official MENA news agency reported.
In the canal city of Suez, troops fired live rounds into the air to stop protesters from storming a police station in the city centre.
Protests also broke out in the central cities of Qena and Assiut, a security official said, adding that 55 people had been arrested nationwide.
Egypt's cabinet, which held crisis talks for several hours before moving en masse to the headquarters of the ruling Supreme Council of the Armed Forces (SCAF) for another meeting, said in a statement that parliamentary elections scheduled for November 28 would go ahead.
Throughout the day, sporadic clashes erupted near the interior ministry on the outskirts of Tahrir Square, which was covered by clouds of tear gas and littered with stones and glass.
In makeshift hospitals SET up in mosques around the square, demonstrators were treated for tear gas inhalation and injuries from rubber bullets and birdshot.
The SCAF, in a statement read out on state television, said it "regretted" what was happening. It said it was committed to the elections timetable.
Earlier Mohsen al-Fangari, a member of the council, insisted the election would go ahead as planned and that the authorities were able to guarantee security.
"We will not give in to calls to delay the elections. The armed forces and the interior ministry are able to secure the polling stations," Fangari told a talk show on the Egyptian satellite channel Al-Hayat.
Several prominent political figures and intellectuals, including former UN nuclear watchdog chief Mohamed ElBaradei, earlier issued a call for a delay to the legislative polls.
They submitted a new transition roadmap which would see an elected constituent assembly draft a constitution and then a presidential election would be held, followed by parliamentary polls.
The recent street protests have seen the return of riot police, the branch of the interior ministry most used by the Mubarak regime in its crackdown against protesters but rarely deployed since.
Friday's rally, which grouped Islamist and secular activists, called on the military to hand power to a civilian government. It also demanded more control over the constitution the new parliament is to draft.
Protesters called for the withdrawal of a government document that proposes supra-constitutional principles, which could see the military maintain some control over the country's affairs and keep its budget from public scrutiny.
The military says it will hand over power after a presidential election, which has yet to be scheduled.
Friday's demonstration passed without incident, but when demonstrators returned to the square on Saturday, they were met with violence by security forces.
On Saturday, medics announced the deaths of Ahmed Mahmoud, 23, who sustained a bullet wound to the chest in Cairo, and Baha Eddin Mohammed Hussein, 25, hit by a rubber bullet in Alexandria as protests spread.
In Brussels, the European Union called on Egypt to respect human rights.
"I urge calm and restraint and condemn the use of violence in the strongest terms," the EU's foreign policy chief Catherine Ashton said in a statement.
"Law and order must be ensured in a manner respectful of human rights," she added.