A search operation was launched by police, paramilitary forces as well as the Army and security around important installations was strengthened.
A forest guard was injured when they fired at him.
"After they were intercepted, they ran into a forest area between Jhajar Kotli and Nagrota. They spotted a forest guard, wearing a uniform and fired at him. He was injured and is stable," said Senior Superintendent of Police (SSP), Jammu, Vivek Gupta.
Though the men managed to escape, the driver and the conductor of the truck was caught.
Piecing together events of the morning from the interrogation of the driver, from Budgam in central Kashmir, officials said the trio infiltrated from the Kathua-Sambha border early Wednesday morning. They boarded the truck at Chak Dayala, a village about two to three kilometres from the international border.
The Special Task Force of the state police has taken the driver and his aide to the place in Jhajar Kotli where they were picked up, the officials said.
The three terrorists are believed to be part of the Jaish-e-Mohammed and had entered India to carry out a 'fidayeen' (suicide) attack, a senior official said.
"The recoveries, including medicines and dry fruits, made from the truck suggest that they are here to carry out a terror attack," he said.
Gupta added that an AK assault rifle and three magazines were seized from the truck.
Using the bypass road, the truck attempted to flee at a security checkpoint near Jhajar Kotli and was intercepted by security personnel after a few metres, officials said, giving details.
They said the men crossed over to the India side through a 'nallah', or drain.
"This is being frequently used. The issue has been flagged but the BSF, which is mandated to man the international border, disputes it every time," an official said.
A high alert was issued for areas along the Jammu-Srinagar national highway and the Jammu region after the incident.
The last time a terror incident happened in the Jammu region of the 294 km highway was in August 2015 when Lashker-e-Taiba terrorists fired at a Border Security Force (BSF) convoy, killing two personnel.
(This story has not been edited by Business Standard staff and is auto-generated from a syndicated feed.)