The gunmen attacked a mobile Indian army patrol in the state's western Shopian district, The Hindu reported on Thursday, citing a local army spokesman.
Troops returned fire and the operation is ongoing, according to the spokesman.
A separate shooting incident took place in a village near Kulgam, where militants fired on security forces. The fighting also continues.
Violence in the disputed Kashmir region intensified last year, with Indian servicemen and bases often being the main target of militant attacks. India has blamed Pakistan for allegedly allowing gunmen to cross over from its territory. Both nations lay claims to Kashmir.