The justice minister said he thought President Mohamed Mursi would agree with a proposal from the highest judicial authority to curb the scope of new powers. Mursi was "very optimistic Egyptians would overcome the crisis", his spokesman said.
But the protesters, some camped in Cairo's Tahrir Square, have said only retracting the decree will satisfy them, a sign of the deep rift between Islamists and their opponents that is destabilising Egypt nearly two years after Hosni Mubarak fell.
"There is no use amending the decree," said Tarek Ahmed, 26, a protester who stayed the night in Tahrir, where tents covered the central traffic circle. "It must be scrapped."
One person has been killed and about 370 injured in clashes between police and protesters since Mursi issued a decree on Thursday shielding his decisions from judicial review, emboldened by international plaudits for brokering an end to eight days of violence between Israel and Hamas in Gaza.
Mursi's political opponents have accused him of behaving like a dictator and the West has voiced its concern, worried by more turbulence in a country that has a peace treaty with Israel and lies at the heart of the Arab Spring.
Mursi's administration has defended his decree as an effort to speed up reforms and complete a democratic transformation. Leftists, liberals, socialists and others say it has exposed the autocratic impulses of a man once jailed by Mubarak.
Mursi's opponents have called for a protest on Tuesday and leading leftist, Hamdeen Sabahy, vowed peaceful demonstrations would continue until the decree was "brought down", saying Tahrir would a model of an "Egypt that will not accept a new dictator because it brought down the old one".
"President Mursi is very optimistic that Egyptians will overcome this challenge as they have overcome other challenges," presidential spokesman Yasser Ali told reporters, shortly before the president started his meeting with members of Egypt's highest judicial authority, the Supreme Judicial Council.
The Supreme Judicial Council has hinted at a compromise, saying Mursi's decree should apply only to "sovereign matters". That suggests it did not reject the declaration outright.
Justice Minister Ahmed Mekky, speaking about the council statement, said: "I believe President Mohamed Mursi wants that."
Legal experts said "sovereign matters" could be confined to issues such as declaring war or calling elections that are already beyond legal challenge. But they said Egypt's legal system had sometimes used the term more broadly, suggesting that any deal could leave wide room for interpretation.
And any deal with a judiciary dominated by Mubarak-era judges, which Mursi has pledged to reform, may not placate them.
Though both Islamists and their opponents broadly agree that the judiciary needs reform, his rivals oppose Mursi's methods.
The Supreme Constitutional Court was responsible for declaring the Islamist-dominated parliament void, leading to its dissolution this year. One presidential source said Mursi was looking for ways to reach a deal to restructure that court.
A group of lawyers and activists has also challenged Mursi's decree in an administrative court, which said it would hold its first hearing on Dec. 4. Other decisions by Mursi have faced similar legal challenges brought to court by opponents.
The protesters are worried that Mursi's Muslim Brotherhood aims to dominate the post-Mubarak era after winning the first democratic parliamentary and presidential elections this year.
Banners in Tahrir called for dissolving the assembly drawing up a constitution, an Islamist-dominated body Mursi made immune from legal challenge. Many liberals and others have walked out of the assembly saying their voices were not being heard.
Only once a constitution is written can a new parliamentary election be held. Until then, legislative and executive power remains in Mursi's hands, and Thursday's decree puts his decisions above judicial oversight.
One Muslim Brotherhood member was killed and 60 people were hurt on Sunday in an attack on the main office of the Brotherhood in the Egyptian Nile Delta town of Damanhour, the website of the Brotherhood's Freedom and Justice Party said.
The party's offices have also been attacked in other cities.
One politician said the scale of the crisis could push opponents towards a deal to avoid a further escalation.
"I am very cautiously optimistic because the consequences are quite, quite serious - the most serious they have been since the revolution," said Mona Makram Ebeid, a former member of parliament and prominent figure in Egyptian politics.
Mursi's office repeated assurances that the steps would be temporary, and said he wanted dialogue with political groups to find "common ground" over what should go into the constitution.
But though the presidency has called for dialogue, that has been rejected by members of the National Salvation Front, a new opposition coalition of liberals, leftists and other politicians and parties, who until Mursi's decree had been a fractious bunch struggling to unite.
The Front includes Sabahy, Nobel Peace Prize laureate Mohamed ElBaradei and former Arab League chief Amr Moussa.
The military has stayed out of the crisis after leading Egypt through a messy 16-month transition to a presidential election in June. Analysts say Mursi neutralised the army when he sacked top generals in August, appointing a new generation who now owe their advancement to the Islamist president.
Though the military still wields influence through business interests and a security role, it is out of frontline politics.