Curfew continued in south Kashmir's Pulwama, Kulgam and parts of Shopian district and restrictions were still imposed in Srinagar, Badgam, Kupwara and Baramulla.
"Preventive measures shall continue to maintain law and order," a senior police officer said here.
Despite the restrictions, some private transport was witnessed in many uptown and outskirts areas of Srinagar city.
Private and public transport were also seen on the Srinagar-Jammu and Srinagar-Leh national highways.
Separatists have extended their protest shutdown till August 5.
Many markets in interior areas of Srinagar and other cities and towns of the Valley opened on Sunday evening.
Separatists have asked people to resume normal activities after 6 p.m.
Separatist leaders including Syed Ali Geelani, Mirwaiz Umer Farooq and Yasin Malik continued to remain under house arrest.