The Supreme Council of the Armed Forces said in a statement and on TV, it regretted “the deaths of martyrs from among Egypt’s loyal sons”, and vowed to bring those responsible to justice.
The unrest, which began on Friday and has claimed 35 lives, was sparked by a looming election following the ousting of President Honi Mubarak.
The country was rife with street battles through the night, especially around the fortified interior ministry off Tahrir Square in Cairo.
Clashes have also taken place in Alexandria. They are the longest outbreak of violence since the 18-day uprising that toppled
Mubarak in February.
The protesters have rejected a pledge to speed up transition to civilian rule, vowing to continue until Egypt’s military rulers stand down.
“He goes, we won’t,” one banner in Tahrir Square read in a reference to the head of the military council, Field Marshal Mohamed Hussein Tantawi.
Ahead of the elections due Monday, senior generals have urged Egyptians not to compare them to the former regime of Mubarak, insisting they were not seeking to cling to power.
The protests have continued despite an attempt by Field Marshal Tantawi to defuse the situation by promising presidential elections by the end of June, six months sooner than planned.
The UN Commissioner for Human Rights, Navi Pillay, has condemned the “clearly excessive use of force” by Egypt’s security forces during the clashes, calling for an independent inquiry into the deaths.
In Alexandria protests have been smaller than in Cairo, but one protester said clashes were continuing early on Thursday outside the security headquarters.
Public opinion on the parliamentary elections is divided. Some Egyptians want elections to go ahead unhindered, while others believe the military must be swept from power first.
The main opposition group, the Muslim Brotherhood, is expected to perform well in the elections.
Throughout the week, demonstrators have thrown stones in their battles with police, and have spoken of gunshots and injuries of deaths from live bullets.
But Interior Minister Mansour el-Essawy said security forces were only firing tear gas.