CAIRO — With a constitutional assembly on the brink of collapse and protesters battling the police in the streets over the slow pace of change, President Mohamed Morsi issued a decree on Thursday granting himself broad powers above any court as the guardian of Egypt’s revolution, and used his new authority order the retrial of Hosni Mubarak.

Mr. Morsi, an Islamist and Egypt’s first elected president, portrayed his decree as an attempt to fulfill popular demands for justice and protect the transition to a constitutional democracy. But the unexpected breadth of the powers he seized raised immediate fears that he might become a new strongman. Seldom in history has a postrevolutionary leader amassed so much personal power only to relinquish it swiftly.

“An absolute presidential tyranny,” Amr Hamzawy, a liberal member of the dissolved Parliament and prominent political scientist, wrote in an online commentary. “Egypt is facing a horrifying coup against legitimacy and the rule of law and a complete assassination of the democratic transition.”

Mr. Morsi issued the decree at a high point in his five-month-old presidency, when he was basking in praise from the White House and around the world for his central role in negotiating a cease-fire that the previous night had stopped the fighting in the Gaza Strip between Israel and Hamas.