Separately, two suspected Muslim fighters were killed in fighting with Indian security forces on Monday.
Acting on a tip, police raided the village of Khor late on Sunday, triggering a gun battle that continued through the night, said K Rajendra Kumar, inspector-general of Kashmir police.
Early Monday, police found the body of Abdullah Bhai in a house in the village, Kumar said, adding that security forces were still engaged in a standoff with another suspected fighter who was also holed up in the village.
Kumar said the slain fighter was identified as a commander of a Pakistan-based armed pan-Islamic group, Lashkar-e-Tayabba, and was allegedly linked to bombers who carried out the 29 October attacks on two New Delhi markets and a bus, killing 60 people.
Kumar’s claim could not be independently verified.
Indian police and intelligence agencies have blamed Lashkar for the October attacks, a charge the armed group denies.
Khor is about 40km north of Srinagar, the summer capital of Indian Kashmir.
In another gun battle, security forces killed at least two suspected members of Lashkar-e-Tayyaba and recovered arms and ammunition in a forest some 70km north of Jammu, the state’s winter capital, said a city police officer who spoke on condition of anonymity because he is not authorised to speak to the media.
About a dozen armed groups have been fighting for Kashmir’s independence or its merger with Pakistan since 1989. The separatist insurgency has killed more than 66,000 people.
India and Pakistan have fought two wars over Kashmir, a Himalayan region divided between them, since their independence from Britain in 1947.