In scenes reminiscent of the popular uprising that unseated predecessor Hosni Mubarak, police fired tear gas at stone-throwers following protests by tens of thousands on Tuesday against the declaration expanding Mr Mursi's powers and putting his decisions beyond legal challenge.
Protesters say they will stay in Tahrir until the decree is withdrawn, bringing fresh turmoil to the nation and delivering a new blow to an economy already on the ropes.
Egypt's Cassation and Appeals courts said they would suspend their work until the constitutional court ruled on the decree.
A spokesman for the Supreme Constitutional Court, which declared the Islamist-led parliament void earlier this year, said it felt under attack by the president.
He said: "The really sad thing that has pained the members of this court is when the president of the republic joined the campaign of continuous attack on the Constitutional Court."
Senior judges have been negotiating with Mr Mursi about how to restrict his new powers, while protesters want him to dissolve an Islamist-dominated assembly that is drawing up a new constitution and which Mr Mursi protected from legal review.
Any deal to calm the streets will likely need to address both issues. Many protesters want the cabinet to be sacked too.
Mr Mursi's administration insists his actions were aimed at breaking a political log-jam to push Egypt more swiftly towards democracy, an assertion his opponents dismiss.
Two people have been killed in violence since the decree, while low-level clashes between protesters and police have gone on for days near Tahrir.