Egyptian Vice President Mahmoud Mekky has proposed a dialogue on disputed articles of the draft constitution and said a breakthrough in resolving the crisis was imminent.
"I am completely confident that if not in the coming hours, in the next few days we will reach a breakthrough in the crisis and consensus," Mr Mekky said.
Earlier the country's President Mohammed Mursi returned to work a day after the presidential palace came under siege from thousands of protesters.
Angry crowds gathered at the palace furious at his drive to push through a new constitution after temporarily expanding his own powers.
The Health Ministry said 35 protesters were wounded and the Interior Ministry said 40 policemen were hurt in clashes around the palace yesterday.
While they fired tear gas when protesters breached barricades to reach the palace walls, riot police appeared to handle the disturbance with restraint.
"There must be consensus," Mr Mekky told a news conference. He expected a dialogue to begin soon, he said, adding the demands of opposition protesters must be respected.
According to his plan, all parties would respect the document until new parliamentary elections that are expected early next year.
At that point, parliament would initiate steps towards a formal amendment of the constitution.
A presidential source said Mr Mursi was back in his office even though up to 200 demonstrators had camped out near one entrance to the palace in the northern Cairo district of Heliopolis overnight.
Traffic was flowing normally in the area where thousands of people had protested the night before, and riot police had been withdrawn.
The rest of Cairo was calm, despite the political furore over Mr Mursi's 22 November decree handing himself wide powers and shielding his decisions from judicial oversight.
The Islamist leader says he acted to prevent courts from derailing a newly drafted constitution that will go to a referendum on 15 December, after which Mr Mursi's decree will lapse.
The crowds had gathered in what organisers had dubbed a "last warning" to Mr Mursi.
"The people want the downfall of the regime!" they chanted, roaring the signature slogan of last year's uprising that ousted Hosni Mubarak.
But the "last warning" may turn out to be one of the last gasps for a disparate opposition which has little chance of stopping next week's vote on a constitution drafted over six months and swiftly approved by an Islamist-dominated assembly.
Facing the gravest crisis of his six-month-old tenure, the Islamist president has shown no sign of buckling under pressure, confident that the Muslim Brotherhood and its Islamist allies can win the referendum and a parliamentary election to follow.