The incident happened in Gool, 230 kilometres south of the main city of Srinagar, the officers said on condition of anonymity.
“It is mayhem. Six are dead and dozens injured. The death toll could rise further,” said one.
Protesters had gathered outside the Border Security Force (BSF) station to demonstrate against an incident involving troops at a mosque on Wednesday evening, witnesses said.
The troops had entered the mosque in Gool to complain about the loud recitation of prayers by worshippers during the holy month of Ramazan, the witnesses told AFP.
Worshippers gathered outside the security force station from early Thursday to protest at the incident.
“The BSF soldiers fired indiscriminately, downing protesters left, right and centre,” one witness who declined to be identified told AFP by phone from the nearby village of Dharam.