"A captain of 10 para regiment was martyred when security forces entered the building on Sunday morning in which militants are holed up," a senior police official told IANS.
"Heavy firing exchanges are going on in the area and the Srinagar-Jammu highway has been closed for safety purposes."
A paramilitary central reserve police force (CRPF) spokesman has denied the media reports that three CRPF troopers were killed in the gunfight so far.
"We have lost two troopers. The rumour about the death of the third trooper is wrong," he said.
"The number of injured CRPF troopers has, however, risen to 13 after three more troopers got injured during the operation."
With the death of the army official, the toll in the gunfight has risen to four.
This includes a civilian, Abdul Gani Mir, gardener of the Jammu and Kashmir Entrepreneurship Development Institute (JKEDI).
Mir succumbed to bullet injuries sustained during the gunfight on Saturday.
A group of heavily armed militants on Friday evening attacked a bus which was part of a CRPF convoy on the Srinagar-Jammu national highway.
Two CRPF troopers had died and ten were injured in this attack.
After the attack, the group of guerrillas comprising three to five, believed to belong to Lashkar-e-Taiba (LeT) outfit, entered the JKEDI complex near the highway where around 120 trainees and staff were present, a senior police official said.
"All the staff members and trainees were safely evacuated before launching t he operation against the holed up militants," the official said.