Three security force personnel were injured in the initial exchange of firing, the officials said.
The civilians have been identified as Sharjeel Ahmed Sheikh, Bilal Ahmed Tantary and Faisal Illahi.
A soldier and three civilians were killed as militants clashed with security forces on Wednesday in Jammu and Kashmir's Kulgam district, triggering violent street protests, officials and witnesses said.
A civilian was killed while as another sustained injuries in clashes with government forces which erupted near the gunfight site. "Two Lashkar-e-Taiba militants are believed hiding in the area", said the police.
In occupied Kashmir, Indian troops, in their fresh act of state terrorism, martyred two Kashmiri youth in Kulgam district, today.
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The doctor added that the hospital received 30 injured persons having bullets, pellets and other injuries due to teargas shells.
A joint team force of the Army and the CRPF launched a cordon in the area following inputs about the presence of a few militants. The encounter started between militants and government forces started late last night in Khudwani.
By then, however, one soldier and three civilians had been killed while two security personnel and over 40 civilians were injured.
Mobile internet services have been reportedly snapped in parts of Kulgam and Anantnag areas.