Police said the deaths occurred in two separate clashes, which broke out a day after Indian forces claimed to have shot dead four top fighters.
The first gunfight erupted on Saturday evening in the southern district of Pulwama, when two Indian border guards and one militant were killed during an encounter.
In the second incident, three Indian army soldiers and six Kashmiri fighters were killed in northern Baramulla district of Kashmir.
Among the dead Indian security personnel was an officer.
Separatist violence has racked Kashmir despite a recent thaw between nuclear neighbours India and Pakistan.
More than a dozen armed groups are seeking the region’s independence from Indian rule. India accuses Pakistan of extending clandestine support to the armed groups and the two countries very nearly came to a war in mid-2002.
The two nations have fought three wars over Kashmir in the past.
Around 38,000 people have died in the Kashmir conflict since 1989. Separatist groups however put the toll much higher.