The encounters took place in Anantnag and Baramulla districts.
Militants opened fire on a patrol party of army at Beewra in Srigufwara area of Anantnag district this morning, a police official said.
He said the army personnel retaliated, triggering a gunbattle.
One militant, identified as Basit Ahmad Dar, was killed in the encounter.
Dar had recently joined Hizbul Mujahideen militant outfit.
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In another counter-insurgency operation, a militant -- believed to be a foreigner -- was killed in Bomai area of Sopore in north Kashmir's Baramulla district, the official said.
However, police sources said the deceased is believed to be Abu Bakar, a top commander of Lashkar-e-Toiba militant outfit.
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