RNA - Shesh Paul Vaid, director general of police, said that the three men died in a shootout after government forces surrounded a densely-populated neighborhood in the old part of Srinagar, the region’s main city.
A young man also died after he was hit by an armored vehicle.
A paramilitary trooper was also injured during the exchange of fire.
Witnesses said hundreds of residents hit the streets near the site of the firefight, shouting slogans of freedom from Indian rule.
The protests and clashes later spread to other areas of the city's old quarters.
Since last year, gun battles between government forces and pro-independence fighters seeking an end to Indian rule in the disputed valley have become more frequent.
The fighting has so far this year left a total of 110 dead, including 20 civilians and 28 security forces personnel.
New Delhi has deployed some 500,000 soldiers to the disputed region to further boost the security of the borderline and enforce a crackdown on pro-independence demonstrations in its share of Kashmir, where anti-India sentiments are high.
New Delhi is also preparing to deploy elite commandos from its National Security Guard, known as Black Cats, to the disputed territory.
According to Press TV, Kashmir lies at the heart of a bitter territorial dispute since India and Pakistan became independent in 1947. Cross-border frictions have recently flared up between troops from the two neighbors along the disputed de facto border in Kashmir. The two sides have accused each other of provocation.
New Delhi and Islamabad both claim the region in full, but rule parts of it. Pakistan administers one-third of Kashmir, with the remaining two-thirds under India’s control.
Thousands of people have been killed in the unrest in Kashmir over the past two decades.
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