Three security personnel were injured in the exchange of fire, they said.
Additional Director General of Police, Jammu Zone, Mukesh Singh said the encounter broke out between terrorists and security forces in Narla village.
“One terrorist and an Army soldier were killed while three security personnel two Army jawans and one special police officer were injured in the gunfight,” he said.
The security forces launched a search and cordon operation in the forested Patrada area on Monday evening and fired a few rounds after noticing suspicious movement of two persons, the officials said.
However, they said, both the suspects managed to escape from the scene taking advantage of the darkness and thick foliage. They left behind a rucksack along with some clothes and other articles that were recovered by the search parties.
The cordon and search operation was extended to nearby areas, including Bambel and Narla, to track down the terrorists, the officials said, adding the search operation in the area was underway.
A Defence spokesperson said a brave Army dog, a six-year-old female Labrador from 21 Army Dog Unit, also lost its life in the encounter while saving its handler.
“Army dog Kent was at the forefront of ‘Operation Sujaligala’. Kent was leading a column of soldiers on the trail of the fleeing terrorists. It came down under heavy hostile fire. While shielding its handler, it laid down its life in the best traditions of the Indian Army,” he said.
The border districts of Rajouri and Poonch have witnessed several encounters this year, resulting in the killing of about 26 terrorists and 10 security personnel.
Most of the terrorists were killed while attempting to sneak into Indian territory from across the border, according to officials.