The authorities have also imposed restrictions in the old city areas of Srinagar, the summer capital of the state and the urban hub of the separatist campaign.
A police officer told IANS that curfew would continue in Bandipora town, Hajin, Naidkhai, Sumbal and other parts of the district.
Restrictions on pedestrian and vehicular movement were clamped in parts of Srinagar where police and the Central Reserve Police Force were deployed in riot gear.
On Friday, a youth, Farhat Ahmad Dar, was killed in Naidkhai area of Bandipora district in police firing.
A magisterial probe has been ordered into the killing.
Separatist leaders, including Mirwaiz Umer Farooq and Muhammad Yasin Malik, called for a shutdown in the Kashmir Valley Sunday to denounce the youth's killing.