As well as ordering retrials for Mubarak-era officials responsible for violence during the uprising against his rule, the decree shielded from legal challenge an Islamist-dominated assembly writing Egypt's new constitution.
It gave the same protection to the upper house of parliament, dominated by Islamists allied to Mursi, and assigned the president new powers that allowed him to sack the Mubarak-era prosecutor general and appoint a new one.
It stated that all decisions taken by Mursi until the election of a new parliament were exempt from legal challenge.
Presented as a move to "protect the revolution," the decree won immediate praise from Mursi's allies but stoked fears among secular-minded Egyptians that the Muslim Brotherhood and its allies aim to dominate the new Egypt. It seemed likely to deepen the divisions that have plagued the post-Mubarak era.
"These decisions will feed discord in Egyptian politics and will be far from creating a favourable climate for restoration of economic growth," said Mustapha Kamal Al-Sayyid, a professor of political science at Cairo University.
Leading liberal politician Mohamed ElBaradei, writing on his Twitter account, said Mursi had "usurped all state powers and appointed himself Egypt's new pharaoh."
But Mahmoud Ghozlan, spokesman for the Brotherhood, described the move as "revolutionary and popular."
The decree appeared to remove any uncertainty still hanging over the fate of the assembly writing the constitution. The body has faced a raft of legal challenges from plaintiffs who dispute its legality.
Critics say its popular legitimacy had been further called into doubt by the withdrawal of many of its non-Islamist members, who had complained their voices were not being heard.
The constitution is a crucial element in Egypt's transition to democracy. New parliamentary elections will not be held until the document is completed and passed by a popular referendum.
The decree also gave the body an additional two months to complete its work, meaning the drafting process could stretch until February, pushing back new elections.
A number of political forces condemned the decree and said the president "robbed the people and institutions of all the rights and powers," in a statement they issued later at night.
The move to order a retrial of Mubarak-era officials will likely be popular among those who feel that revolutionary justice has yet to be served.
Mubarak, 84, was sentenced to life in prison in June for failing to prevent killings that occurred during the uprising that led to his February 11, 2011 downfall. He has been held in a prison hospital since his sentence was handed down.
Critics have faulted the process by which he and other officials were put on trial. One of the problems, they say, was that the Mubarak-era prosecutor general had not been replaced.
Mursi had tried to replace Abdel Maguid Mahmoud, the man sacked on Thursday, in October. The move kicked up a storm of protest from judges who said the president had exceeded his powers and was threatening their independence.
Mursi got around the problem this time by giving himself the power to appoint a new prosecutor general, Talat Abdullah, whose swearing-in was shown on state television.
In a statement broadcast on state TV, Abdullah vowed to "work with colleagues at the public prosecution's office to uphold justice and eradicate oppression."
Ali said a new prosecution office would be established to "protect the revolution" and made up of judges who would be given powers to order investigations and collect evidence.
Heba Morayef, Egypt director for Human Rights Watch, said: "Egypt needed judicial reform and the public prosecutor is a Mubarak holdover, but granting the president absolute power and immunity is not the way to do it."