A police officer said the militants were killed after they fired upon a joint party of police and army near Galganzer, Zacheldara in Rajwar area of Handwara on Monday evening. "In the exchange of fire, two terrorists were killed".
A police spokesman said the slain militants were identified as Toib of Sopore and Ashiq of Palhallan Pattan.
Police officials are trying to ascertain their identity and affiliation, The Hindu reported.
"At both these places, searches are going on".
Security forces, deployed in strength, have sealed all exit points and started search operation, they said, adding that so far no one has been arrested.
Four of his family members including father, two brothers and an aunt were also injured in the attack.
A video of a Congress worker hailing from south Kashmir's Shopian district and being tortured by militants has gone viral on social media.