Security forces said 10 men were killed in an area close to an army base that was attacked on Sunday.
Fighting broke out in two different locations along the Line of Control, the disputed de facto border with Pakistan-administered Kashmir.
It comes after 10 weeks of protests in which almost 90 people have died.
Army spokesman Lt-Col Rajesh Kalia said soldiers intercepted two large groups of suspected rebels who had entered an Indian-administered area of Kashmir.
Why India needs cool heads after Kashmir attack
The attack on Sunday at the army's Uri cantonment by four gunmen, in which 18 soldiers were killed, was the deadliest against Indian security forces in Kashmir for years.
India later accused Pakistan of masterminding the attack, with Home Affairs Minister Rajnath Singh labelling the country a "terrorist state".
Pakistan denied the allegations, dismissing it as a knee-jerk response by India and a "blatant attempt" to deflect attention from human rights abuses in Kashmir.
It comes as violent protests against Indian rule in the disputed region continue, with a strict curfew imposed.
Both India and Pakistan claim all of Muslim-majority Kashmir in its entirety but only control parts of it.
Eleven people, including a soldier, have died in clashes between troops and suspected militants in Indian-administered Kashmir, the army says.