The Valley-wide strike called by the separatist leadership to protest the deaths evoked mixed response.
"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.
However, the movement of people was allowed on the Srinagar-Jammu national highway passing through south Kashmir.
"There is no restriction on the movement of people anywhere else in the Valley but security forces have been deployed in sensitive areas to keep a tight vigil on anti-social elements," he said.
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Four local militants and two army men were killed in the encounter that lasted several hours yesterday.
Meanwhile, the strike called by separatist groups to protest the civilian killings evoked mixed response today.
Though most of the shops, fuel stations and other business establishments were shut across Srinagar, public as well as private transport vehicles were plying in many areas, officials said.
Inter-district transport was also operational on many routes connecting various districts of the Valley to Srinagar. However, less public transport was visible in rural areas of the Valley, they said.
Chairmen of both factions of Hurriyat Conference -- Syed Ali Geelani and Mirwaiz Umar Farooq -- and JKLF chief Mohammad Yasin Malik had called for a complete shutdown today and 'Kulgam Chalo' on February 15 to protest the civilian killings.