Some people had their own agendas to exploit the youth revolution for their own interests, Suleiman said, indicating that they may be businessmen, foreign elements or militia infiltrators.
Neither the president nor his son Gamal Mubarak will run for the presidency, Suleiman reiterated.
Prime Minister Ahmed Shafiq on Thursday offered "apologies" over Wednesday night's clashes and promised that offenders would be held accountable, and said that he was ready to talk with protestors face to face in the Tahrir Square.
"Once more, I apologize for all the victims," Shafiq said in an interview with the Egyptian state TV, stressing "all the perpetrators who violated the law and killed or injured people in peaceful demonstrations will go through tough investigations."
"I pledge to maintain the security of the people and bring them to normal life," the prime minister added.
Arab League Secretary General Amr Moussa on Thursday said the transitional period in Egypt started with Mubarak's announcement not to run for the presidency after the end of his current term in office.
In a released statement, Moussa regretted that the peaceful protests turned violent after some outlaws joined them to wreak havoc in the Egyptian street, the official MENA news agency reported.
Meanwhile, on the opposition side, former IAEA chief Mohamed ElBaradei said Thursday in a TV interview that "Egyptian protesters lost confidence in the Mubarak regime, (and) we couldn't start dialogue with the new government until Mubarak leaves."
In light of the escalation of violence, the White House confirmed on Thursday that the United States is discussing with Egyptians a "variety of different ways" of moving toward a peaceful transition in Egypt.
Tommy Vietor, spokesman for the White House National Security Council, said President Barack Obama has said now is the time to begin "a peaceful, orderly and meaningful transition, with credible, inclusive negotiations."
"We have discussed with the Egyptians a variety of different ways to move that process forward, but all of those decisions must be made by the Egyptian people," he said.
Earlier, the New York Times reported that the White House is in close talks with Egyptian officials on Egypt's power transition, and according to one of the proposals, Mubarak would hand power over to a transitional government led by his deputy Suleiman, who would then begin a process of constitutional reform with the support of the military.
The proposal also calls on the transitional government to invite members from a broad range of opposition groups, including the Muslim Brotherhood, in preparations for the general elections in September, it said.
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