Mr. Morsi announced the date after Egypt's Islamist-dominated assembly handed its final draft of the constitution to him late Saturday.
The draft constitution mandates the principles of Sharia law as the main source of legislation.
Earlier Saturday, tens of thousands of Islamists demonstrated across Egypt in support of Mr. Morsi and the draft constitution. Supporters gathered outside Cairo University and elsewhere, waving Egyptian flags, raising banners and demanding the implementation of what they called “God's law.”
The Muslim Brotherhood called for the rallies.
Also Saturday, thousands of protesters demonstrated in Cairo's Tahrir Square for a ninth straight day against the president and the draft constitution. They have been voicing opposition to a decree giving Mr. Morsi extraordinary powers.
The Egyptian leader caused a political uproar when he granted himself sweeping new powers that bar the judiciary from challenging his decisions. Mr. Morsi said Thursday the decree will end immediately once the people vote on the constitution.
Mr. Morsi has been waging a battle with Egypt's judges, many of whom are opponents of the Muslim Brotherhood that dominates Egypt's parliament. The president is a former member of the once-banned group.
On Sunday, Egypt's top judicial power is expected to rule on whether to dissolve the country's Islamist-led assembly.
In recent days, about 30 Christian, liberal and secular members have boycotted the assembly to protest what they call the hijacking of the process by Islamists loyal to President Morsi.
At least two people have been killed and hundreds injured in Egypt's nationwide demonstrations. VoA.