"Curfew has been imposed in entire Kulgam district and Shopian town to maintain law and order in the wake of the killings yesterday", a police official said.
At least 17 persons, including nine militants, six soldiers, and two civilians, were killed since Monday in three different gunfights in the Valley.
They said the intelligence input was clear that militants were hiding in a house in the village following which a cordon was thrown around the locality so that no militant escaped.
Two of them belonged to Kashmiri separatist group Hizbul Mujahideen while the other two were Pakistan-based Lashkar-e-Taiba (LeT) operatives, the police said.
Shops, public transport and other business establishments remained closed.
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Jammu and Kashmir police chief SP Vaid said the security forces were fully alert to meet all challenges and separatist efforts to repeat 2016's unrest would not succeed.
Kashmir Valley was tense on Monday, a day after eight people including four local militants, two Army jawans and two civilians were killed and almost twenty people were injured in a fierce gunfight and subsequent clashes between irate crowds and security forces in a remote village of southern Kulgam district.
Two army soldiers were also killed in the gunfight. One man died and about 12 were injured when the security forces opened fire on the crowd.
The Valley-wide strike called by the separatist leadership to protest the deaths evoked mixed response. The National Conference demanded an investigation into the encounter.