Police fired tear gas at stone-throwing youths in streets around Cairo's Tahrir Square.
A 52-year-old protester died after inhaling tear gas -- the second death since last week's decree.
Protesters also turned out in Alexandria, Suez, Minya, and cities in the Nile Delta.
Critics have accused Morsi of acting like a dictator by issuing his decree, which protects his decisions from judicial review.
Morsi says the decree was necessary to speed up democratic change and will be rescinded after parliamentary elections.
The Muslim Brotherhood canceled a rally in support of Morsi on November 27 in a bid to ease tensions.