Morsi issued a decree stating that all decisions he has made since taking office are not subject to review or appeal, The Washington Post reported.
Shortly after Morsi named Talaat Ibrahim Abdallah to succeed Abdel Meguid Mahmoud as prosecutor general, Abdallah announced he would retry Mubarak, former Interior Minister Habib al-Adly and other former Mubarak-era officials on charges of killing protesters, al-Masry al-Youm reported.
Mubarak and Adly were sentenced in June to life in prison for their roles in the killing of protesters in Tahrir Square last year, but Adly's aides were acquitted. Egypt's Truth Seeking Committee said in October Mubarak, Adly and his aides should be retried.
"If a danger arises that threatens the January 25 revolution," the decree issued by Morsi read, the president "can take any procedures and preparations that he sees necessary to face this danger," the Post reported.
Some Egyptian TV commentators immediately suggested the decree suggested Morsi was creating a "dictatorship," and protesters began to gather in Tahrir Square -- some holding posters with images of Morsi and Mubarak.
Morsi supporters assembled at another location in Cairo to demonstrate in favor of the proclamation, the Post said.
Morsi canceled plans to attend a summit in Pakistan to monitor the cease-fire between Israel and Palestinians.
"Mr. Morsi took this decision because of the need to monitor internal developments in Egypt and also to monitor the commitments of all parties regarding the ceasefire in Gaza," a presidential statement said.
Vice President Mahmud Mekki will attend the Developing Eight Islamic summit in Islamabad instead.
Egyptian security officials said they confiscated three rockets in northern Sinai that may have been en route to Gaza, Ahram Online reported. The rockets were found about 9 miles from the border with the Gaza Strip.
Sappers deactivated the medium-size rockets which were to be smuggled into Gaza via tunnels in Rafah, a security source from the North Sinai Security Directorate told the site.