Morsi declared unilaterally that until a new constitution is decreed all presidential decisions would be immune from legal challenge.
"The president can issue any decision or measure to protect the revolution," said his statement, read out on television by his personal spokesman, Yasser Ali.
"The constitutional declarations, decisions and laws issued by the president are final and not subject to appeal."
The announcement caused outrage. Mohammed ElBaradei, the former head of the International Atomic Energy Agency who returned to Egypt to become a leader of the liberal opposition, said: "Morsi today usurped all state powers and appointed himself Egypt's new pharaoh. A major blow to the revolution that could have dire consequences."
Morsi's move was designed to short-cut a series of stalemates to Egypt's constitutional transition from the dictatorship of Hosni Mubarak.
The committee drawing up the new constitution, which is dominated by members of Islamist groups including Morsi's own Muslim Brotherhood, is facing repeated challenges to its legality. His declaration nullifies those challenges, and extends by two months the time available for it to do its work.
He also announced the sacking of the chief prosecutor, Abdel-Maguid Mahmoud, one of the last so-called "remnants" of the Mubarak regime.
Mahmoud's failure to win convictions against many of those alleged to be responsible for the shooting of protesters during and after last year's revolution has led to continuing protests, particularly this week, the anniversary of a particularly bloody demonstration.
Morsi announced there would be retrials in many of those failed prosecutions, possibly including that of Mubarak himself, who was sentenced to life for failing to stop the crackdown but who many opponents believe should have been found guilty of ordering it.