The militants opened fire from within the house where they were holed up, making it hard for Army men to enter.
Also three security personnel have been killed and two injured.
Soon after the encounter ended, hundreds of people, amid pro-freedom and anti-India slogans, gathered near the site and started pelting stones at the forces who retaliated with pellets and teargas.
Authorities thus had made heavy deployment of police and paramilitary forces to prevent rallies.
On Sunday, Military forces were involved in a gunfight with a group of militants holed up in a home in south-Kashmir, the policeman said.
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In the operation, almost four militants have been neutralised while two others are still holed up inside the house in Kulgam's Yaripora, ANI reported. Of the two civilians killed, one persons identified as Mushtaq Ibrahim succumbed to his injuries at district hospital Anantnag after he was injured in the clash between people and the forces.
Police also recovered the body of a civilian, reportedly the young son of the house owner, from the debris.
Reports said that curfew like restrictions were imposed in Kulgam and Shopian town to thwart possible protests. The other suffered injuries when security forces fired on protesters and died in a hospital. Encounter still underway in south Kashmir.
The trend of people thronging the encounter sites started in February past year when more than dozen army soldiers, including an officer, were injured when a mob of around thousand people threw stones at them in Ashmuqam village in Anantnag district, 69 kilometres south of Srinagar. Strings of terror-related incidences have taken place since then.
The administration has beefed up security in "sensitive areas" in the region after separatist leaders called for a strike to protest against the civilian deaths.