Calm was restored to Egypt on Saturday, after a mass overnight protest against President Mohamed Morsi ended peacefully, but the underlying political crisis dividing the country persisted.

More than 100 protesters remained outside the presidential palace in Cairo, watched over by soldiers who used tanks and barbed wire to block roads leading to the compound.

Overnight, more than 10,000 people had massed in the palace square in a noisy demonstration, tearing aside a barbed-wire barricade and yelling for Morsi to step down.

The crowd gradually dwindled to a hard core of protesters, repeating a pattern of nightly protests this week that peaked each evening.

But there was no sign of them faltering in their opposition to the Islamist president and the sweeping new powers he decreed for himself last month, or to a controversial draft constitution Morsi is putting to a referendum he has called for December 15.

"I'm ready to die. All these guys are ready to die. I don't want violence but if they try to oppress us, there has to be a stand," said one protester who camped out overnight, Mustafa el-Tabbal, 27.

Although around 2,000 Morsi supporters from the president's Muslim Brotherhood held a rival rally just a few kilometres (miles) away, there was no repeat of the violent clashes between the two sides of Wednesday night. Then, seven people died and more than 640 were hurt.

Since the clashes, Morsi has struck a defiant tone, defending his decree and the referendum.

But his camp has also made some conciliatory gestures to the mainly secular opposition, seen as attempts to de-escalate the confrontation.

Morsi offered to hold talks with the opposition on Saturday, but that was rebuffed by the National Salvation Front coalition ranged against him.

One of the Front's leaders, Mohamed ElBaradei, a former UN atomic agency chief and Nobel Peace laureate, stressed late Friday that dialogue could only happen if Morsi agreed to "repeal the decree" and postpone the referendum.

Vice President Mahmud Mekki said Morsi "could accept to delay the referendum," but only if the opposition guaranteed it would launch no legal challenge to the decision.

Under Egyptian law, a president is compelled to hold a referendum two weeks after formally being delivered its text.

Mekki said early voting for Egyptians overseas that had been scheduled for Saturday had now been pushed back to Wednesday.

And on Saturday, the Cairo prosecutors' office told AFP that all 133 people arrested during Wednesday's clashes had been released.

The state newspaper Al-Ahram said in its Saturday edition that there was "an opening in the constitutional crisis."

The independent newspaper Al-Masry al-Youm, though, headlined that "The protesters held up a 'red card' to the president in front of the presidential palace."

The opposition fears Morsi's "power grab" and referendum aim to push the country towards a more Islamic state, based on the slender mandate he won in a June election.

Their slogans and mobilisation recalled the uprising that toppled Egypt's autocratic leader of 30 years, Hosni Mubarak, early last year.

Morsi's backers in the Muslim Brotherhood, in turn, fear that judiciary, with its many Mubarak-era appointees, is plotting to block the reforms they are trying to push through.

The political crisis has unsettled the United States, which was cautiously warming to Morsi as a foreign policy partner but which has little direct leverage over his domestic issues.

US President Barack Obama this week spoke by telephone to Morsi to express his "deep concern" over the deadly turn of events in Cairo and to advocate dialogue with the opposition.