Protests demanding an end to Hosni Mubarak's 30-year rule is set to continue in Egypt.
Protesters on Friday prepared for big demonstrations to mark the "Day of departure" for the beleaguered president.
The developments come as the New York Times reports, quoting US officials and Arab diplomats, that the US administration is discussing with Egyptian officials a proposal for Mubarak to resign immediately and hand over power to a transitional government headed by Omar Suleiman, the newly appointed vice-president.
The Egyptian president, for his part, says he has had enough and is ready to go but fears chaos if he resigns now.
Mubarak's remarks, to an American TV network on Thursday, came as two days of clashes between protesters and his supporters on Cairo's streets left at least 13 people dead and hundreds injured.
Ahmed Shafiq, Egypt's new prime minister, said the interior minister should not obstruct Friday's peaceful marches. The interior ministry has denied it ordered its agents or officers to attack pro-democracy demonstrators.
Mubarak's government has struggled to regain control of a nation angry about poverty, recession and political repression, inviting the Muslim Brotherhood - Egypt's most organised opposition movement - to talks and apologising for Wednesday's bloodshed in Cairo.
The confrontation extended to Thursday in central Cairo where armed Mubarak loyalists fought pro-democracy demonstrators.
"I am fed up. After 62 years in public service, I have had enough. I want to go," Mubarak, 82, who remains inside his heavily guarded palace in Cairo, said in the interview with ABC News.
"If I resign today, there will be chaos."
Asked to comment on calls for him to resign, he said: "I don't care what people say about me. Right now I care about my country."
Mubarak blamed the Muslim Brotherhood for Wednesday's violence and said his government was not responsible for it.
"I was very unhappy about yesterday. I do not want to see Egyptians fighting each other," Mubarak told ABC.
In a move to try to calm the situation, Suleiman, the vice-president, said on Thursday the Muslim Brotherhood had been invited to meet the new government as part of a national dialogue with all parties.
An offer to talk to the banned but tolerated group would have been unthinkable before protests erupted on January 25, indicating the gains made by the pro-democracy movement since then.
But scenting victory, they have refused talks until Mubarak goes.
Protesters in Tahrir Square, dominated now by a youthful hard core including secular middle-class graduates and mostly poorer Muslim Brotherhood activists, barely listened, saying the concessions were too little and too late.
Opposition actors including Mohamed ElBaradei, the former UN nuclear watchdog head, and the Muslim Brotherhood said again that Mubarak, who wants to stay on until elections scheduled for September, must go before they would negotiate with the government.
"We demand that this regime is overthrown, and we demand the formation of a national unity government for all the factions," the Muslim Brotherhood said in a statement broadcast by Al Jazeera.
The government's overture came after Shafiq, the prime minister, apologised for Wednesday's violence and the breakdown in law and order.
Shafiq also said he did not know who was responsible for the bloodshed, blamed by protesters on undercover police.
The army's role in shaping events is crucial. Only on Thursday did soldiers set up a clear buffer zone around the square to separate factions after having stood by. That did not prevent new clashes as opposing groups pelted each other with rocks.
Doctors in makeshift hospitals at the scene said at least 10 people were dead and 800 wounded after armed men and stick-wielding Mubarak supporters attacked protesters on the streets. The UN estimates that number to be much higher.
Close to the Egyptian Museum, men fought with rocks, clubs and makeshift shields, as army tanks made intermittent efforts to intervene.
There were sporadic clashes throughout Thursday as the army fanned out to separate the two sides and allowed thousands more protesters to enter their camp in the square.
An Al Jazeera online producer in Cairo said: "The battle for downtown Cairo took on an almost medieval quality, with protesters erecting makeshift barricades and building homemade catapults to launch rocks at each other."
He described the contrast between both sides' tactics as striking. "The pro-democracy protesters organised themselves, building walls and seizing strategic locations; the pro-Mubarak crowd mostly advanced in a mob, hurling rocks and then retreating under return fire," he said.
There were several reports of foreign journalists being arrested or harassed. Dozens of them had their equipment confiscated.
Among the many detained were correspondents for the New York Times, Washington Post and Al Jazeera. The New York-based Committee to Protect Journalists (CPJ) said late on Thursday that in just the past 24 hours, it had recorded 24 detentions of journalists, 21 assaults and five cases in which equipment was seized.
Angry men carjacked an ABC News crew and threatened to behead the journalists, but the crew managed to talk its way free, according to the network.
Al Jazeera said three of its journalists were detained by security forces, four were attacked and another was missing. It reported on Thursday night that the arrested journalists had been released.
The channel, which the Egyptian authorities accuse of favouring the protesters, also said its equipment have been stolen and destroyed and its broadcast signal disrupted across the Arab world.
CPJ said on Wednesday that violence against journalists was part of a series of deliberate attacks and called on the Egyptian military to provide protection for reporters.
Shahira Amin, a senior journalist at Nile Television, a government-owned network, walked out on Wednesday in anger that state TV was not broadcasting enough of the protests and clashes in Tahrir Square.
Though less numerous than earlier in the week, there were demonstrations on Thursday in Suez and Ismailia, industrial cities where inflation and unemployment have kindled the sort of dissent that hit Tunisia and which some believe could ripple in a domino effect across other Arab police states.
There were also protests in the port city of Alexandria.
Source: Al Jazeera and agencies