"Of the two killed terrorists one is a foreign terrorist and the other a local of Jaish militant outfit, " Deputy inspector General of Police, South Kashmir, S P Pani said.
The gunfight started on Monday evening after the armed forces launched an operation in Batmuran village of the district.
The fighting stopped Tuesday after two militants were killed and a police official and a soldier were injured, police said.
The police said that the woman died in the crossfire between militants and forces during the encounter. But clashes continued between rock-throwing protesters and troops who fired bullets, shotgun pellets and tear gas. Forty civilians have been killed during protests against security forces in the state since the beginning of 2017. In the morning Jan, 30, was killed when she was hit by a bullet near the encounter site.
Eyewitnesses said that the Indian forces also blew three houses and two cowsheds during the gunfight using explosives, besides torching a vehicle and a motorcycle. Three militants were also killed in that operation.
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A woman was injured during the exchange of fire and she succumbed to her injuries later on.
The killings have invited sharp criticism from the resistance leadership led by octogenarian senior leader Syed Ali Geelani, and including Mirwaiz Umar Farooq.
In a statement, the leadership said that the "ongoing killings" of innocent men and women by Indian trigger-happy forces is agonizing. The hoteliers raised massive pro-Pakistan, anti-India and freedom slogans.
Over 200 militants, 75 police and soldiers and at least 40 civilians have died this year, the deadliest since 2010. Last year, 15 civilians were killed and 285 were injured in similar events.
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