One policeman was also injured in the encounter.
The incident took place at around 5.45 a.m., when a police team was randomly checking vehicles near the Nagrota toll post on the Jammu-Srinagar national highway and intercepted a Srinagar-bound truck.
Speaking to , Jammu and Kashmir Director General of Police (DGP) Dilbag Singh said: "The module is from a fresh infiltration that could have happened from the International Border in Jammu last night."
He further said: "It was a group of four Pakistani terrorists who were going to Kashmir. The truck was stopped as part of regular checking in Nagrota."
One terrorist was shot down in the first exchange of fire in which a policeman was also injured. A truck conductor was arrested, but the other three terrorists ran into the forest.
In the subsequent firing, two more terrorists were killed and two overground workers of the terrorists arrested.
A large quantity of arms and ammunition has been recovered from them, and the three who have been arrested were being interrogated.
Sources said that it seems to be a Jaish-e-Mohammed module, which had infiltrated from the Hiranagar - Kathua International Border in Jammu.
According to sources there were seven people, including four terrorists in the truck when it was intercepted by the police.
Police sources also said that some locals were trying to help the terrorists to move from Jammu to Srinagar.
(Zaffar Iqbal can be contacted at zaffar25@gmail.com)
( With inputs from IANS )