Egypt's top judges have accused President Mohammed Mursi of staging an "unprecedented attack" on the judiciary.
The president passed a decree earlier this week granting himself extensive new powers.
It includes a bar on any court dissolving the constituent assembly, which is drawing up a new constitution.
Thursday's decree sparked angry demonstrations, and attacks on offices of Mr Mursi's Islamist FJP party.
The president has said he is acting to protect the revolution.
In a statement, the Supreme Judicial Council called his move "an unprecedented attack on the independence of the judiciary and its rulings," and called on him to reverse it.
Judges and prosecutors in Egypt's second city Alexandria have gone on strike in protest, saying they will not return to work until the decree is reversed.
The BBC's Jon Leyne in Cairo says the response of the judges has been tough, if fairly predictable.
There had been reports that the council was about to disband the constituent assembly for a second time, he added, a move that could seriously derail the transition to democracy and further delay new parliamentary elections.
This, in turn, could deter Egypt's political leaders from taking tough decisions while they wait for the vote.
Mr Mursi also sacked his prosecutor general on Thursday and gave himself the sole power to appoint a new one.
His replacement moved quickly to reopen criminal investigations into ousted President Hosni Mubarak, his family, and former regime officials.
Our correspondent says that element is likely to be popular, as although Mubarak is serving a long jail term for ordering the killing of protesters during the 2011 uprising, many officials were acquitted, creating deep resentments.
The ruling also bans any challenging of the president's decisions and laws.
Both critics and supporters of Mr Mursi have staged rallies since the decree. Overnight, crowds gathered in Cairo's Tahrir Square, vowing to stage a sit-in.
A large opposition rally is also planned for Tuesday.
The US said earlier that Mr Mursi's move had raised concerns in the international community.