More than 20 Egyptian rights groups have called on President Mohammed Mursi to withdraw the decree granting himself extensive new powers.
The 22 groups signed an open letter saying the president "has dealt a lethal blow to the Egyptian judiciary".
Opposition politician Mohamed El Baradei has said there could be no dialogue with Mr Mursi while the decree, announced on Thursday, was in force.
According to the decree, no authority can revoke presidential decisions. It includes a bar on dissolving the assembly drawing up a new constitution.
"These actions undermine the rule of law and the pillars of justice and exploit presidential powers to protect the interests of a particular political group," said signatories to the letter posted on the Cairo Institute for Human Rights website.
The president's office says the decree is temporary.
The BBC reports that the announcement of the decree sparked angry demonstrations and attacks on offices of Mr Mursi's Islamist Freedom and Justice Party (FJP) party.
Critics and supporters of Mr Mursi have staged rallies since the decree was announced, with both sides planning rival demonstrations for Tuesday.
The Muslim Brotherhood, the Islamist movement that backs the FJP, has called for demonstrations across Egypt later on Sunday, reports say.
On Saturday, Egypt's judges denounced the decree as an "unprecedented attack" on the judiciary.
After an emergency meeting, the Judges' Club - the union which represents judges throughout the country - called for "the suspension of work in all courts and prosecution administrations".
Police fired tear gas to disperse crowds as supporters of the judges faced off against pro-Mursi demonstrators who tried to disrupt the meeting.