Police fired tear gas – as they had on Friday evening – as protesters hurled stones and set a school near the interior ministry on fire.
Mr Morsi was unrepentant over his move to make his decisions unchallengeable in the courts. That ruling was announced on Thursday, in the wake of his success in negotiating a ceasefire deal between Hamas and Israel. His Muslim Brotherhood backers called for a mass rally in his support on Tuesday.
But Mr Mosri came under pressure from Egypt's judges, who had been sidelined in the declaration. He stopped all further legal challenges to the committee drawing up a new constitution, sacked the prosecutor-general and decreed that all his own decisions were beyond challenge until a new parliament is elected.
The Supreme Judicial Council held an emergency meeting to declare that the decision was "an unprecedented attack on the independence of the judiciary and its rulings".
"The decisions and declarations announced on November 22 raise concerns for many Egyptians and for the international community," the US state department also said.
It added: "One of the aspirations of the revolution was to ensure that power would not be overly concentrated in the hands of any one person or institution."
On Friday, demonstrators ransacked and burned down offices of the Brotherhood's political front, the Freedom and Justice Party, in Alexandria, Port Said and Ismailiya.
"Out! Out!" the crowd chanted. "The people want the downfall of the regime."
Mr Morsi told a crowd of supporters gathered in front of the presidential palace that he was trying to stop a "minority" which he said was attempting to "block the revolution".
He alleged that money stolen under the old regime was being used to fund new protests, including by "thugs" – a politically loaded term suggesting that the pro-democracy protesters were the same as Mr Mubarak's hired henchmen.
"There are weevils eating away at the nation of Egypt," he told them. Mr Morsi said he was trying to assure "political stability, social stability and economic stability".
He added: "I have always been, and still am, and will always be, God willing, with the pulse of the people, what the people want, with clear legitimacy."
The protesters have been dominated by the young, secular liberals and leftists who triggered last year's revolution but were later sidelined by Islamist groups, including the Muslim Brotherhood and the more purist Salafis.
However, Mr Morsi was only able to win 52 per cent of the vote in the election that brought him to power in June – which opponents say is not enough to give him the mandate necessary for the radical steps he has taken. They now believe they can capitalise on widespread dissatisfaction with the speed of economic and social progress since Mr Morsi became president.
"I reject all these decisions," said Reem Ahmed, 32. She was holding up a placard saying, "I am a dead man," in solidarity with two victims of earlier protests this week, who were shot by police. She said: "The country is in danger. We gave Mr Morsi a chance. But now we have had enough."