Egyptian opposition protesters have demonstrated outside the presidential palace in Cairo, after breaking through a barricade erected by security forces.
Tens of thousands had gathered near the palace after rejecting a call for dialogue by President Mohammed Morsi.
Opposition leaders say Mr Morsi has offered no concession on his decisions to expand his powers and to put a new draft constitution to a referendum.
A top official later said the president could conditionally postpone the vote.
Under Egyptian law, referendums must be held two weeks after being formally presented to the president.
However, Vice-President Mahmud Mekki said Mr Morsi could delay the 15 December plebiscite if the opposition guaranteed agreed not to challenge the move on those grounds later, AFP news agency reports.
In a separate development, the election commission postponed the planned voting for Egyptians living abroad.
It said the voting - which had been due to begin on Saturday - would now begin on Wednesday at the request of the foreign ministry.
Earlier on Friday liberal and secularist opponents of the president gathered near the presidential palace.
They then cut through barbed wire and surged up to the outer walls of the palace, where many sprayed graffiti.
Meanwhile supporters of Mr Morsi held their own march in the capital, vowing vengeance at a funeral for men killed in clashes earlier in the week.
"Egypt is Islamic, it will not be secular, it will not be liberal!" the crowd chanted.
The main opposition movement, the National Salvation Front, said it would not take part in talks Mr Morsi had offered to hold on Saturday, in an effort to resolve the spiralling crisis.
Nobel prize winner Mohamed ElBaradei, the movement's chief co-ordinator, posted a message on his Twitter account calling on political groups to shun all dialogue with Mr Morsi.
"We [want] a dialogue not based on an arm-twisting policy and imposing fait accompli," his message read.
Two other opposition groups, the liberal Wafd party and the National Association for Change, said they were also boycotting the talks.
The president angered his opponents on Thursday when he refused in a televised statement to withdraw his new powers - announced in a decree issued last month - and delay the referendum.
Mr Morsi said that if the constitution were voted down, another constituent assembly would be formed to write a new draft.
Critics say the draft, drawn up by a body dominated by Morsi-supporting Islamists, was rushed through parliament without proper consultation and does not do enough to protect political and religious freedoms and the rights of women.
The BBC's Jon Leyne in Cairo says the growing tensions reveal deep divisions within the Muslim Brotherhood.
Whenever there is talk of compromise, the movement's hardliners seem to win the battle, our correspondent reports.
Earlier this week the presidential palace was the scene of bloody clashes, in which five people died and hundreds were injured.
Late on Thursday, opposition supporters ransacked the Muslim Brotherhood's Cairo headquarters and set it on fire.
On Friday rival protesters between supporters and opponents of the president were reported in a number of Egyptian cities, including Alexandria in the north and Asyut in the south.