The killings were the first since mobile phone services were restored as part of a gradual relaxation of measures taken to crush freedom struggle in occupied Jammu and Kashmir.
New Delhi had cut off telephone and internet lines before it revoked occupied Jammu and Kashmir’s special rights on August 5, striking down long-standing constitutional provisions for the Muslim-majority region.
A security lockdown is still largely in place and broadband and mobile internet connections remain unavailable to most Kashmiris.
"Three terrorists were killed and the bodies were retrieved from the site of the encounter," Kashmir police said in a statement. "Incriminating material, including arms and ammunition, was recovered."
Neither the soldiers or police suffered casualties, according to the police sources, who spoke on condition of anonymity as they were not authorised to talk to the media.
Security forces imposed travel restrictions near the site of the gun battle to prevent unrest, the sources said.
In a separate incident in Pulwama district, a migrant worker from Chhattisgarh state, in central India, was shot dead in an execution-style killing, police said.
The brick kiln labourer was walking along a railway track in the Kakapora area when he was stopped by two people. "He was shot in the head," a police official said, declining to be named.
In another incident, a fruit merchant was killed and another critically wounded when gunmen fired at them in the Shopian district of south Kashmir.
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