Clashes and attacks killed more than 1,000 people across Egypt after the security forces cleared two Cairo sit-ins belonging to supporters of Mr Morsi.
Since the unrest spiked much of Egypt has been under a military-imposed curfew.
Responding to citizens' demands, the government said in a statement on Saturday that the 11 hour-long curfew would be reduced to nine hours.
However, the full curfew would remain in place on Fridays, the first day of the Egyptian weekend.
The reduction was announced a day after calls for protests by Mr Morsi's Muslim Brotherhood largely fizzled out.
In recent days, Cairo has begun to regain a sense of normality.
But the capital officially remains in a state of emergency that gives security forces broad powers of arrest.
Pushing ahead with a transition plan, a 10-member panel of legal experts appointed by the interim government finished proposing changes to the 2012 constitution today.
The military had suspended the charter drawn up by an Islamist-dominated assembly.
Portions of the proposed changes were leaked to reporters on Saturday, drawing criticism from both sides.
The liberal National Salvation Front criticised the proposed electoral system for parliamentary elections, which would favour single candidates over party lists.
They fear this could allow the former ruling class of the Hosni Mubarak period to drift back into power.