"The army, after a tip-off, launched an operation in the Kupwara forests and shot dead 10 terrorists. One soldier also lost his life in the firefight," spokesman Colonel Dharam Adhikari said.
He said the 11-hour gun battle took place in the Kandi area of Kupwara district, northwest of Srinagar.
Police said two more fighters were killed in a nearby village in Kupwara and another died in the neighbouring Baramulla district.
Earlier four Indian soldiers were killed and seven injured by a landmine, the army said.
The troops, who belonged to the army's counter-insurgency wing, the Rashtriya Rifles, were travelling through the wooded Salar area of central Anantnag district when their vehicle ran over the mine, an army spokesman said.
Soldiers were rushed in and sealed off the area. Kashmir's largest separatist group Hizb al-Mujahidin claimed responsibility for the blast in a telephone call to local media.
Separatist violence has continued in the troubled region despite recent peace moves between India and Pakistan, which went to the brink of war over Kashmir in mid-2002.