The operation began early today in the Durama hills range across the Simsang River in the district where suspected assailants responsible for the killing were hiding in one of the outfit's camp, they said.
State police's Swift Weapons and Tactic (SWAT) personnel and the CRPF CoBRA commandos swung into action and were exchanging fire with the militants in the jungle, Inspector General of Police G H P Raju said.
A 35-year-old woman was shot at point blank range when she resisted molestation and rape attempt by GNLA men. The gruesome murder, in which the woman's head was blown up, was committed in front of her husband and children on Tuesday evening at remote Raja Rongat village in South Garo Hills district.
The GNLA has openly acknowledged the killing and accused the woman of being a police informer.
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The outfit in the statement also accused the editor of an influential Garo vernacular weekly of spreading "baseless and concocted" rumours.
The GNLA is an outlawed militant outfit co-founded by a senior police deserter Champion Sangma and Sohan D Shira, a militant, in 2010.
The outfit is active in all the five districts in the Garo Hills region and is involved in kidnapping, extortion and killing of both civilians and security forces.