Mursi made the constitutional declaration yesterday that granted him far-reaching powers and also ordered retrials of officials involved in the killing of protesters during the 2011 mass uprising against the Mubarak regime.
The decision came a day after the President was praised by world leaders for brokering a truce between Hamas and Israel.
Yesterday's constitutional declaration has sparked a fierce debate in the country, with supporters calling it "revolutionary" and detractors slamming the sweeping powers it grants Egypt's presidency as a "coup".
The opposition has called for nationwide protests.
The declaration made yesterday also said no court can dissolve the Constituent Assembly, which is drawing up a new constitution.
The Constituent Assembly's timeline for drafting the new constitution has also been extended by two months.
Mursi, 61, also sacked the chief prosecutor and ordered the re-trial of people accused of attacking protesters when ex-President Mubarak held office.
According to the declaration, all investigations into the killing of protesters or the use of violence against them will be re-conducted. Trials of those accused will be re-held.
All constitutional declarations, laws and decrees made since Mursi assumed power on June 30, 2012, cannot be appealed or cancelled by any individual, or political or governmental body, according to the declaration.
The president is authorised to take any measures he sees fit in order to preserve the revolution, to preserve national unity or to safeguard national security.
The essence of the declaration guards decisions of Mursi against annulment by the judiciary and gives him almost autocratic rule.
Egyptian opposition leader Mohammed ElBaradei accused Mursi of acting like a "new pharaoh". ElBaradei said the new declaration effectively placed the president above the law.
