The two countries are currently attending a regional trade summit in Nepal, but some observers say their rivalry has overshadowed attempts to strike a deal.
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Thursday's fighting happened near an Indian army base in the town of Arnia, an area that saw deadly fighting between Pakistani and India troops in September.
A senior police official in Jammu told the BBC that about five militants gained access to the disused bunker.
After locals informed the border guard, troops were called in and began to surround the area, he said.
A gun battle then erupted, lasting for approximately six hours.
Civilians in the area - which is only 3km (2 miles) from the international border with Pakistan - were evacuated and schools closed down, according to the Associated Press news agency.
Thousands of people have been killed in Kashmir since an anti-India uprising began in 1989.
In recent years violence has abated from its peak in the 1990s, but the causes of the insurgency are still far from resolved.
A ceasefire agreed in 2003 remains in place, but the nuclear-armed neighbours often accuse each other of violating it.
Last month both sides issued warnings to one another after violence in the region saw at least 19 civilians killed.