Five rebels and Indian policeman killed in Kashmir
A policeman was also killed by unknown gunmen in a separate attack in the disputed Himalayan region.
Fighting began late on Saturday when troops, acting on intelligence, cordoned off two villages in the southern Shopian and Bijbehara areas, Inspector General Vijay Kumar told reporters.
He said two soldiers were wounded in Shopian.
A policeman working in a counter-insurgency unit was shot in the western Magam area, a local police officer said.
He blamed anti-India militants for the killing but gave no further details.
Kashmir is divided between India and Pakistan and claimed by both in its entirety.
Earlier this year, the two countries reaffirmed their 2003 ceasefire accord. However, inside the Indian-held portion, a crackdown by Indian forces as well as attacks by rebels have continued.
New Delhi describes the Kashmir militancy as Pakistan-sponsored terrorism. Pakistan denies the charge, and most Kashmiris consider it a legitimate freedom struggle.
Mr Kumar said one of the three suspected militants killed in Shopian was a teenage boy, and that a rifle and two pistols were recovered after the gun fight.
Other police officers said he was 16 years old and had joined the insurgency only a few days earlier.
In Bijbehara, Mr Kumar said Indian forces killed two militants and recovered two rifles, adding that the two were responsible for killing an army soldier on Friday.
Residents said troops torched a civilian home during the gun battle.
Authorities buried the dead militants in a remote graveyard about 75 miles (120km) from their ancestral villages, a police statement said.
Under a policy started in April 2020, Indian authorities have buried more than 200 alleged Kashmiri rebels in unmarked graves, denying their families proper funerals.
The policy has added to widespread anti-India anger in the region.
At least 15 militants, two policemen and an army soldier have been killed so far this month.
Many Muslim Kashmiris support the rebel goal that the territory be united either under Pakistani rule or as an independent country.
Tens of thousands of civilians, rebels and government forces have been killed in the conflict.
The youngest militant to die in the three-decade insurgency was a 14-year-old boy killed by Indian soldiers alongside another teenager in late 2018.
The best videos delivered daily
Watch the stories that matter, right from your inbox