Barricades have been put in place to curb civilian movement while security forces personnel are present in public enforcing the restrictions. The gunfight also left a civilian dead and four Indian soldiers injured.
Most of India-administered Kashmir remained closed on Monday following violent clashes between separatists and security forces in which some 20 people are feared killed.
Earlier police had said that five militants were killed in Kachdooru but they later revised the figure.
Behind the killing of 12 militants in a day in South Kashmir's Shopian were eight months of reconfiguration and restructuring of armed forces in the area.
Heavy contingents of police and the Central Reserve Police Force (CRPF) were deployed in the restricted areas in Srinagar.
"Two of the killed militants have been identified as Ishfaq Thokar resident of Paddarpora Shopian, Aitmad Hussain Dar resident of Amshipora, Shopian, while the identity of the other two is being ascertained", said a police official.
The terrorists move towards mountainous areas of these districts whenever security forces step up anti-terrorism operations.
Reports said the highway town of Banihal, Khari, Tethar and Chareel in Ramban district observed complete shutdown to mourn the death of 17 people, including 13 militants, in three separate gunfights.
KCC&I has been continuously demanding that no solution lies in using unbridled powers against civilian population resulting in more casualties, it said.
Despite a ceasefire agreement that was reached between India and Pakistan in November 2003, sporadic skirmishes continue in Kashmir. Inspector General of CRPF Zulfikar Hassan pointed out that people came in large numbers at the encounter site in Shopian. Some six civilians have received bullet injuries.
Monday to protest the killings.
Almost two dozen persons were injured in fresh clashes in many parts of Valley while a 22-year-old youth injured critically at Kangan area of central Kashmir's Ganderbal district.
In Srinagar, authorities imposed restrictions in parts of the city to maintain law and order as a separatist leaders had also called for a protest shutdown.
Kashmir has been divided between nuclear-armed India and Pakistan since the end of British colonial rule in 1947, but both claim it in full.
Khaqan Abbasi emphasized that Indian attempts to label the legitimate Kashmir struggle as terrorism could not deter the valiant people of Jammu and Kashmir from their demand of exercising their right to self-determination in accordance with United Nations resolutions.
Thousands took to the streets over the weekend in support of the rebels, who have been fighting for decades for independence or for a merger with Pakistan. India accuses Pakistan of arming and training the rebels, a charge Pakistan denies.
Almost 70,000 people have been killed in the uprising and the ensuing Indian military crackdown.