A cordon and search operation was launched by army in Zaipora area of Shopian during the night following intelligence inputs about the presence of militants there, a police official said.
He said during the search operation, the militants fired upon the party in which three army personnel were injured.
The injured were taken to Army's 92 base hospital in Srinagar, where two of them, including a major, succumbed, the official said, adding that the other jawan is undergoing treatment.
The search operation at Zaipora is on, the official said.
Meanwhile, in Kulgam district of south Kashmir, two militants were killed on Thursday morning in an encounter with security forces, the police said. A police official said one of the slain militants was involved in an attack on a bank cash van in the district on 1 May this year in which five policemen and two bank guards were killed. On 1 May, one of the attackers was arrested while another had managed to escape. The van was returning to a bank in the village of Pumbai in Kulgam district, around 70 kilometres south of the main city of Srinagar, when it had come under fire. The security forces on Thursday recovered two weapons from the site of the encounter.
The encounters have taken place two days after Lashkar-e-Taiba (LeT) divisional commander Abu Dujana was gunned down by security forces after an encounter broke out on Tuesday in south Kashmir's Pulwama district. Another LeT terrorist Arif Lilhaari was also killed in the encounter.
As the security forces were engaged in the counter-militancy operation, over 100 protesters pelted stones on them, an army official had said.
The security forces had launched a cordon and search operation in Hakripora area of Pulwama on Monday night following information about presence of Abu Dujana and his local aide, Arif Lilhaari, in the area.
Dujana hailed from Gilgit Baltistan, which is a part of Pakistan-occupied-Kashmir (PoK). Dujana joined LeT when he was 17.
According to India Today, Dujana first infiltrated into India in 2010 after which he developed LeT's network across Jammu and Kashmir, especially south Kashmir, which has been a hotbed of militancy since the past year.
With inputs from PTI.