President Mohamed Mursi was expected to press ahead on Saturday with talks on ways to end Egypt's worst crisis since he took office even though the country's main opposition leaders have vowed to stay away.
Cairo and other cities have been rocked by violent protests since November 22, when Mursi promulgated a decree awarding himself sweeping powers that put him above the law.
The upheaval in the most populous Arab nation, following the fall of Hosni Mubarak last year, worries the West, in particular the United States, which has given it billions of dollars in military and other aid since Egypt made peace with Israel in 1979, reports Reuters.
Mursi's deputy raised the possibility that a referendum set for December 15 on a new constitution opposed by liberals might be delayed. But the concession only goes part-way towards meeting the demands of the opposition, who also want Mursi to scrap the decree awarding himself wide powers.
On Friday, large crowds of protesters surged around the presidential palace, breaking through barbed wire barricades and climbing on tanks guarding the seat of Egypt's first freely elected president, who took office in June.
As the night wore on, tens of thousands of opposition supporters were still at the palace, waving flags and urging Mursi to "Leave, leave".
"We will stay here for as long as it takes and will continue to organize protests elsewhere until President Mursi cancels his constitutional decree and postpones the referendum," said Ahmed Essam, 28, a computer engineer and a member of the liberal Dostour party.
Vice President Mahmoud Mekky issued a statement saying the president was prepared to postpone the referendum if that could be done without legal challenge.