In the Kashmir part of the state, a large contingent of the Indian army cordoned off the village of Gambru late on Sunday after receiving a tip that several militants had gathered there, said army Colonel Hemant Juneja.
Gambru is 60km (40 miles) north of Srinagar, Jammu-Kashmir's summer capital
The troops came under fire as they approached two houses, starting an all-night gun battle. A soldier and a suspected militant were killed, Juneja said. Later, the army said it had found the body of a second militant.
Three soldiers were wounded, one critically, Juneja added.
Also on Monday, Indian troops identified a group of suspected militants crossing the Line of Control, the de facto frontier between Indian and Pakistani Kashmir, late on Sunday. The ensuing fight killed four infiltrators, Juneja said.
The incident occurred in the Gulmarg area, about 80kms (50 miles) north of Srinagar. There were no army casualties.
India and Pakistan have fought
two wars over Kashmir
Later on Monday, two suspected militants were killed in a gunbattle with paramilitary soldiers in Wangund, an eastern suburb of Srinagar, said Dileep Singh, a spokesman of the Central Reserve Police Force. A soldier was injured in the brief gunbattle, he said.
Elsewhere, police raided a rebel hide-out in the mountainous Sharekhi district late on Sunday, killing a senior militant, identified as Tariq Usman Sheikh, the district commander of the Hizbul Mujahedeen group, said Manohar Singh, the local police chief.
Sharekhi is about 180kms (110 miles) northeast of Jammu, the state's winter capital.
In another incident, police surrounded a group of militants in the Tramda Nari area, about 190kms (120 miles) northwest of Jammu.
Two militants were killed and police continued to battle others, said area superintendent Farooq Khan. Reinforcements have been called in, he said.
More than a dozen rebel groups have been fighting since 1989 for Muslim-majority Kashmir's independence from predominantly Hindu India or its merger with mostly Muslim Pakistan.
The conflict has killed more than 67,000 people.
Kashmir is a Himalayan territory claimed by India and Pakistan and divided between them. Although Jammu territory is not under dispute, India's Jammu-Kashmir state is commonly referred to simply as Kashmir.
The two nuclear-armed neighbours have fought two wars over Kashmir since their independence from Britain in 1947.