The clash happened after the army’s special counter-insurgency force received information that militants were in Keller forest in the southern Kashmir valley, the army said.
The site is around 65km (40 miles) from Pahalgam, where militants last month killed 26 people, mostly male Hindu tourists, sparking the worst fighting between India and Pakistan since 1999.
A “search and destroy Operation” was launched, leading to a clash, the Indian army said on social media.
“During the operation, terrorists opened heavy fire and [a] fierce firefight ensued, which resulted in elimination of three hardcore terrorists,” it said.
India accused Pakistan of backing the “terrorists” it said were responsible for the Pahalgam attack – a charge Islamabad denied. Last week, New Delhi launched missiles at sites in Pakistan it said were hosting the militants.