The violence came a day after diplomats from nearly two dozen countries finished their two-day visit in Indian-administered Jammu and Kashmir.
Three suspected rebels and a policeman have been killed in two gunbattles in India-administered Kashmir while three cops have been killed in a separate attack in the disputed region's Srinagar city.
A gunfight erupted shortly after scores of counterinsurgency police and soldiers launched an operation late Thursday in a village in southern Shopian district following a tip that three militants were there, Inspector-General Vijay Kumar said.
All three were killed in an exchange of gunfire early on Friday, Kumar said. He said police recovered two rifles and a pistol.
Residents said government forces used explosives to blast a civilian house during the fighting, a common tactic by Indian troops in Kashmir.
In another gunbattle, militants killed a policeman and injured another in western Beerwah area early Friday, Kumar said.
The violence on Friday came a day after diplomats from more than 20 countries stationed in India's capital concluded a two-day visit to the region.
Police operation turns gunfight
In a separate incident, rebels killed two police officers in Srinigar city, according to police officials on Friday.
Police said militants sprayed bullets at two policemen near a police station in Srinagar city. Both died later at a hospital.
A short video of the attack circulated on social media shows a man in a pheran, a Kashmiri tunic worn during the winter, taking out what appears to be an automatic rifle and shooting at the policemen.
He then quickly runs away.
Police and soldiers searched the area and later detained a young man for questioning.
No rebel group immediately claimed responsibility for the attack.
Both India and Pakistan claim the divided territory of Kashmir in its entirety. Many Muslim Kashmiris support the rebel goal that the territory be united either under Pakistani rule or as an independent country.
New Delhi blames Pakistan for the militance in the disputed Kashmir. Pakistan denies the charge, and most Kashmiris consider it a legitimate freedom struggle.
More than 50,000 people have died in an uprising against New Delhi's rule in Kashmir that began in 1989, by government count. Others put the toll at well over 100,000.