Muslim-majority Kashmir has been divided between rivals India and Pakistan since their independence from British rule in 1947 and is home to a long-running insurgency.

The firefight broke out after Indian troops moved to check "suspicious movement" near Halkan Gali in Anantnag, resulting in the death of the two militants.

The Indian Army's Chinar Corps said on social media platform X that a joint operation had been launched in the area.

"Terrorists opened indiscriminate fire," the corps said in its statement. "Troops effectively retaliated, resulting in elimination of two terrorists."

At least 500,000 Indian troops are deployed in Kashmir, battling an insurgency that has killed tens of thousands of civilians, soldiers and rebels since 1989.

Last week suspected militants ambushed an army vehicle and killed five people, including three soldiers.

A week before that, gunmen killed seven people near a construction site for a strategic road tunnel to Ladakh, a high-altitude Himalayan region bordering China.

New Delhi regularly blames Pakistan for arming militants and helping them launch attacks, an allegation Islamabad denies.

The army says more than 720 rebels have been killed since Indian Prime Minister Narendra Modi's government cancelled the territory's limited autonomy in 2019.

In early October, Kashmir held its first elections since 2014 for a regional assembly for the territory of some 12 million people.