This was the second gunfight with AGH militants this month and came within a month of the new outfit's commander Zakir Musa's death in a gunfight in Pulwama district.
Director General of Police, Dilbag Singh told reporters that the four militants killed in the Daramdora village of Shopian were locals and belonged to the "Islamic State-inspired" outfit.
Identifying the killed militants as Showkat Ahmed Mir, Rafee Hassan Mir, Suhail Ahmad Bhat and Abdul Azad Ahmad, he said they were led by Showkat Ahmad Mir of Pulwama district and all of them were wanted in many terror-related cases.
Earlier, Defence Ministry spokesman, Colonel Rajesh Kalia had said: "Four terrorists have been killed in Daramdora village of Shopian district. Weapons and other incriminating material have been recovered from their possession."
The gunfight broke out after the security forces started a cordon and search operation in the village.
"The operation was focused on the orchard area. As the security forces tightened the cordon around the militants, they opened fire, triggering the encounter," a police officer said.
As a precautionary measure, authorities had suspended mobile Internet services in Shopian.
Zakir Musa was killed by the security forces in a gunfight in Tral area of Pulwama n May 24. Before he became the first militant commander to head the AGH, Musa had succeeded Burhan Wani, the Hizbul Mujahideen poster boy of homegrown militancy in the Valley.
On June 11, two local militants of the outfit were killed in a gunfight with the security forces in Awneera village of Zainapora area in Shopian. The two were identified as Shakir Ahmad of Shopian and Sayar Bhat of Kulgam district.
( With inputs from IANS )