"A curfew will continue as a preventive measure in Rainawari, Nowhatta, M.R. Gunj, Safa Kadal, Zadibal and Maisuma areas," a senior police officer told IANS.
"The deployed security forces have been instructed to allow the movement of patients and other emergencies in the areas placed under curfew," the officer added.
The curfew was imposed after a youth, Bashir Ahmad, was killed in firing by security forces in Nawa Kadal area of the city Wednesday.
Two people, a youth and a woman, were injured in the firing incident.
Hardline separatist leader Syed Ali Geelani has called for protests after the Friday prayers.
All political parties have condemned the killing of the youth which is being described by the locals as "an unwarranted, excessive use of force against unarmed civilians".
The Central Reserve Police Force (CRPF) has ordered an inquiry into the incident.