The killings on the border came shortly after rival troops pounded each other for five hours with heavy artillery and machine guns along the Line of Control, the cease-fire line that divides Kashmir between India and Pakistan. Despite the heavy fighting, there were no reports of casualties on either side of the border, police said.
Defense Ministry officials in New Delhi described the fighting as routine.
Indian and Pakistani troops routinely shell each other, but there has been a comparative lull since April after leaders of the two countries renewed efforts to resume talks on Kashmir after two years of bitter relations.
Indian soldiers shot and killed five of about 12 militants during a gunbattle after the suspected Islamic rebels were spotted trying to cross into India's side of the Line of Control, about 75 miles north of Srinagar city, a police officer said on condition of anonymity.
In a separate gunfight in the nearby Trehgam region, soldiers killed three rebels, the officer added.
Indian security forces also shot to death five people, described as Bangladeshi civilians, who were crossing the border at Kanachak, 18 miles west of Jammu city, police said.
Bangladeshis often try to illegally enter India via Pakistan to find jobs. No weapons were found on the men's bodies, police said.
In Kashmir Valley, two soldiers and three suspected rebels were killed in a gunbattle in Hachamarg village, about 62 miles north of Srinagar, police said. Two soldiers were wounded.
The South Asian nuclear rivals have fought two of their three wars over Kashmir, a Himalayan region both claim in its entirety.
India accuses Pakistan of training and arming Islamic guerrillas, who cross into the Indian-controlled portion of Kashmir and attack civilian and government targets. Pakistan says it supports the militants' cause of uniting Kashmir with Pakistan, but denies it aids them.
By Mujtaba Ali Ahmad