The police, army and CRPF were all a part of the operation, Vaid said. The search began when they received intelligence that terrorists were hiding in the area.
One of the three terrorists killed is suspected to be from Pakistan.
Authorities have suspended mobile internet services in Kulgam and nearby Anantnag districts to prevent the spread of rumors.
The encounter is still on.
Terrorists had abducted constable who was home on leave
These terrorists are believed to be involved in the killing of Constable Mohammad Salim Shah, who was abducted from his Muthalhama house Friday night. His body was found Saturday in Qaimoh village with multiple bullet injuries.
The special police officer, who had been recently promoted, was undergoing training and was home on leave.
He was the family's sole bread-earner.
Police said Hizbul Mujahideen was involved.
Several similar killings in recent times
Shah was the 25th policeman killed by terrorists in J&K this year, and the third such incident in two months.
Last month, terrorists abducted an army man, Aurangzeb, from his way home for Eid in Shopian. His body was later found in Pulwama.
Earlier this month, police constable Javaid Ahmad Dar was kidnapped from his house in Shopian and killed.