One IAF GARUD was killed and an army man injured in Chandergeer, Hajin area of district Bandipora on Saturday.
The encounter between the security forces and militants is underway, Kalia said. The operation is on an further details are awaited. The Garud Commando is the special forces unit of the IAF. Another soldier was injured in the operation.
Indian Army and police have claimed recovery of weapons and ammunition from the gunfight site.
Defence spokesman Col Rajesh Kalia said six militants, including LeT commander Mahmood Bhai, were killed in the gunfight. He said the slain militants were from Pakistan.
DGP Vaid termed the encounter of the six Lashkar-e-Toiba (LeT) militants as a great success for the security forces.
Authorities had imposed curfew in parts of Srinagar on Saturday as a precautionary measure following killing of an Al-Qaeda terrorist Mugees Mir in a shootout with the police on Friday evening.
During the encounter, clashes erupted in the area between locals and government forces.
Owaid is the third close relative of Lashkar chief Lakhvi who was killed in Kashmir. In 2007, Lakhvi's 20-year-old son Mohammad Qasim was killed in an encounter with the army and J&K police.
Apart from featuring in the National Investigating Agency (NIA)'s most wanted list, Lakhvi is also among the 3 globally prosecuted terrorists named by India and the European Union in their joint statement to combat terrorism.
On November 14, one terrorist was killed by security forces in Jammu and Kashmir's Kulgam district.