Vice President Omar Suleiman told journalists he had invited the Muslim Brotherhood to enter negotiations with the government. He said the Brotherhood remains "hesitant" but underlined that it was a "valuable opportunity" for the movement.
The Brotherhood, the top political opponent of Mubarak's regime, rejected the offer and said only the president's departure and an end to violence would bring them to negotiations.
The vice president also promised that Mubarak's son Gamal would not run to succeed his father in presidential elections in September.
But in an interview with state TV, Suleiman alleged foreign involvement in the agitation. "When there are demonstrations of this size, there will be foreigners who come and take advantage and they have an agenda to raise the energy of the protesters," he said.
Under an onslaught of international condemnation for Wednesday's assault on protesters by pro-Mubarak rioters that sparked the renewed wave of turmoil, the government offered a series of gestures trying to calm the fury.
Prime Minister Ahmed Shafiq apologized for Wednesday's violence and said it would not happen again. But he insisted he did not know who was behind it.
Egypt's public prosecutor issued a travel ban on some ministers from the former government and at least one former ruling party official, and froze their bank accounts, state news agency MENA said.
The ministers are former Interior Minister Habib El-Adly, former Housing Minister Ahmed El-Maghrabi and former Tourism Minister Zuhair Garana. Former National Democratic Party member Ahmed Ezz was also among those banned from leaving the country.
The statement said other officials were also under the ban which would last "until national security is restored and the authorities and monitoring bodies have undergone their investigations."
Protesters and regime supporters fought in a second day of rock-throwing battles in Tahrir Square in downtown Cairo while new lawlessness spread around the city. New looting and arson erupted, and gangs of thugs supporting Mubarak attacked reporters, foreigners and rights workers while the army rounded up foreign journalists.
The United States sharpened its criticism of Mubarak's regime and expressed outrage over violence against protesters, declaring that its once-close partner should set a brisk course for new elections.
President Barack Obama began his remarks at Thursday's National Prayer Breakfast with pointed hopes for better days ahead: "We pray that the violence in Egypt will end and the rights and aspirations of the Egyptian people will be realized."
Lawlessness that had largely eased since the weekend flared anew. A fire raged in a major supermarket outside Sheikh Zayed, a suburb of the capital, and looters were ransacking the building. A residential building neighboring a 5-star hotel on the Nile River Corniche was also ablaze, blocks away from Tahrir. Other fires erupted in the Cairo district of Shubra, north of the center, security officials said.
At least eight people have been killed and hundreds wounded in the fighting in and around Tahrir. Thursday's fighting centered on and under a highway overpass about 500 meters north of the square's center that pro-government attackers had used as a high ground to rain down stones and firebombs.
