Hundreds of protesters were in Tahrir Square, where tents had been set up since Morsi issued a decree last week.
Police fired tear gas to break up protests, CBS News reported.
Morsi declared the courts could not overturn any decree or law issued by him since taking office and said the order would remain in effect until a new constitution is completed.
The decree sparked harsh criticism, with protesters taking to the streets.
More than 260 people have been injured in clashes in Cairo and elsewhere in the country in the recent protests, CNN said, quoting EGYNews.
Farouq Jweideh became the third presidential adviser to resign, a day after the Saturday resignations of Samir Morcos and Sakina Fouad, Egyptian media reported.
About 20 Egyptian rights groups signed a petition demanding the decree be annulled, the BBC reported, and MENA said a million man march in support of Morsi is being planned for Tuesday.
The Muslim Brotherhood -- which strongly backs Morsi's Freedom and Justice Party -- called for demonstrations across the country in support of his decree.
Politician Mohamed ElBaradei said there can be no dialogue with Morsi as long as the new decree remains intact, the BBC said.