The official said a joint mobile vehicle check post (MVCP) near Pohan in Shopian signalled a car to stop, but it did not.
The Army men were fired upon and they retaliated, in which a militant was killed, the official said. He said a weapon and a pouch was found near the militants body.
The official said that when police were called, they found a car some distance away in which three youths were found dead.
However, Srinagar-based defence spokesman Col Rajesh Kalia said the three were over-ground workers and accomplices of the slain militant.
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All the three were locals and residents of Trenz, Pinjoora and Imamsahib areas of Shopian.
The militant killed in the exchange of fire has been identified as Shahid Ahmad Dar, a resident of Jamnagri, Shopian, Kalia said.
Police reached the spot and was carrying out legal formalities, he said.