The two militants allegedly belonging to Lashkar-e-Taiba (LeT) were killed while three troopers were wounded in a firefight with militants in Pulwama town, 30 kilometres from Kashmir summer capital Srinagar.
Vijay Kumar, deputy inspector general of police in Pulwama, also said seven civilians who attacked a military ambulance to protest the killing of the militants were wounded when police fired on them.
A curfew has been imposed on Pulwama, he added.
The officer said the two militants were behind a grenade attack on a taxi in July that led to the death of four women tourists in Kashmir.
One of them was also involved in a grenade attack last month at a liquor store in the Kashmiri city of Jammu, which left one man dead and five others injured, Kumar said.
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They were innocents. No Muslim is criminal anyways.