The encounter broke out between security forces and militants in Naidkhai area of Bandipora after security forces launched a search operation following specific intelligence inputs, an army official said.
He said two militants were killed in the encounter, while an army jawan also lost his life.
The identity and group affiliation of the slain militants is being ascertained, he said.
Meanwhile, the official said, another encounter broke out between militants and security forces in Sopore area of Baramulla district.
A search operation was launched in Tujjar village of Sopore after specific intelligence inputs about the presence of militants in the area, the official said.
He said as the forces were conducting the search operation, the militants fired upon them, triggering an encounter.
Further details of the operation are awaited, the official said.