Protests held over Morsi powers
"The decree is basically a coup on state institutions and the rule of law that is likely to undermine the revolution and the transition to democracy," Mervat Ahmed, an independent activist in Tahrir protesting against the decree, said. "I worry Morsi will be another dictator like the one before him."
Leading liberal politician Mohamed ElBaradei, who joined other politicians on Thursday night to demand the decree was withdrawn, wrote on his Twitter account that Mr Morsi had "usurped all state powers and appointed himself Egypt's new pharaoh".
Almost two years after Mr Mubarak was toppled and about five months since Mr Morsi took office, propelled to the post by the Muslim Brotherhood, Egypt has no permanent constitution, which must be in place before new parliamentary elections are held.
The last parliament, that sat for the first time earlier this year, was dissolved after a court declared it void. It was dominated by the Brotherhood's political party.
An assembly drawing up the constitution has yet to complete its work. Many liberals, Christians and others have walked out accusing the Islamists who dominate it of ignoring their voices over the extent that Islam should be enshrined in the new state.
Opponents call for the assembly to be scrapped and remade. Mr Morsi's decree protects the existing one and extends the deadline for drafting a document by two months, pushing it back to February, further delaying a new parliamentary poll.
Explaining the rationale behind the moves, the presidential spokesman said: "This means ending the period of constitutional instability to arrive at a state with a written constitution, an elected president and parliament."
Thousands of the president's supporters gathered near the presidential palace, some holding up Morsi posters or chanting for him. The Muslim Brotherhood had called for the rally.
Analyst Seif El Din Abdel Fatah said the decree targeted the judiciary which he said had reversed, for example, an earlier Morsi decision to remove the prosecutor. Mr Morsi's new decree protects him from such judicial reversals.
Although many of Mr Morsi's opponents also opposed the sacked prosecutor, who they blamed for shortcomings in prosecuting Mubarak and his aides, and also want judicial reform, they say a draconian presidential decree was not the way to do it.
"There was a disease but this is not the remedy," said Hassan Nafaa, a liberal-minded political science professor and activist at Cairo University.
"I can see from the reaction of the political forces that we are going towards more polarisation between the Islamist front on one hand and all the others on the other. This is a dangerous situation," he said, adding it could spark more street trouble.
The streets have been relatively quiet since Mr Morsi took office, although this week protesters have clashed with police during rallies to mark deadly demonstrations last year.
In June, the then ruling military council issued a decree as Mr Morsi was being elected that sought to rein in his powers, but he struck back in August issuing a decree as president revoking that, giving himself those powers and sacking top generals.
The new army leaders are now appointees of Mr Morsi and have stepped back from politics. The military still wields hefty influence through its huge business interests and security role.
But one analyst said the generals had been "neutralised."