Police said the curfew would continue in some areas of south Kashmir while restrictions under section 144 of the CrPc (Criminal Procedure Code) will remain in force in Srinagar city and other districts.
Overnight protests occurred in Shopian district.
Despite clashes at some places on Monday, some semblance of normal activities of life was noticed in parts of Srinagar city as private vehicles and pedestrian movement was seen almost after three weeks.
Chief Minister Mehbooba Mufti who interacted with members of the civil society in north Kashmir's Baramulla district on Monday, appealed for a collective effort to reach out to the people of Jammu and Kashmir.
Traffic on both the Jammu-Srinagar and Srinagar Jammu national highways resumed during the night.
Train services, educational institutions, banks, post offices and government offices except essential services like health, water supply, electricity, food supplies, police and fire services are shut here for the last 24 days.
Officially imposed curfew and protest shutdown called by the separatists thr ough weekly protest calendars have crippled life in Kashmir since July 9, a day after Hizbul commander, Burhan Wani's death in a gunfight.