"Anyone that has had a hand in creating the violence that we've seen in the past few days will be brought to justice immediately," the prime minister said.
He added, "We say this was not planned, this was not a strategy, this was not a work of the government."
Clashes between the two groups of demonstrators broke out during the night with gunfire and fire bombs raining down on those who want Mubarak to leave office immediately.
The Associated Press reported that soldiers were taking up positions between the two sides and had cleared a bridge of pro-Mubarak forces, but later stepped aside as the anti-Mubarak forces occupied the bridge.
By noon, relative calm had fallen over Tahrir Square, but gunfire broke the lull later in the day.
The clashes reportedly left at least five dead and almost 1,000 wounded.
The Egyptian uprising continued to be felt elsewhere in the region. In Yemen, police opened fire on protesters in the capital of Sanaa. It wasn't clear if the police were firing rubber bullets or live ammunition.
The government also froze the bank accounts of several recently fired ministers, including the hated former interior minister who was in charge when the cops led a bloody crackdown of the marchers.
Today marked the second day of combat between the two sides. It began Wednesday when thousands of pro-Mubarak demonstrators entered the square, including some riding camels and horses and using whips to attack their rivals.
Opposition protesters claimed that those supporting the president were Mubarak's thugs, paid by the administration to disrupt their largely peaceful gathering. The Ministry of Interior denied that security forces were among protesters in Tahrir Square.
The White House condemned the riots, but stopped short of condemning the government for the violence.
President Obama "found the images outrageous and deplorable," White House Press Secretary Robert Gibbs said.
The two battling sides surged forward and back Wednesday. Pavement was broken up and turned into missiles. Veiled women piled stones high onto blankets to be carried to the front.
By late afternoon, petrol bombs appeared, setting several buildings on fire.
Mubarak's announcement Tuesday that he would not run for reelection, but would stay through September, did little to stop protesters calling for his immediate removal.
"My first responsibility is to restore the security and stability of the homeland, to achieve a peaceful transition of power in a way that will protect Egypt and Egyptians, and that will allow for responsibility to be given to whomever the people elect in the forthcoming elections," Mubarak said in his second speech to the nation since the protests began a week ago.
Mubarak said that he will ask the new government to speed up elections, which are scheduled to be held in September.
The situation in Egypt is particularly alarming to the United States because Egypt is one of United States' closest allies in the Middle East. It is only one of two Arab countries that recognizes Israel and has helped broker key peace deals.
Mubarak's government also has been a close U.S. ally in the fight against terrorism.The Suez Canal also is in Egypt, and any instability in the region could be gravely dangerous to U.S. interests in the region.
ABC News' Nasser Atta, Lama Hasan contributed to this report.