A policeman and a rebel were killed in Indian Kashmir on Monday as the troubled region shut down to protest at the weekend shooting of two civilians by the army, a police chief said.

The officer and the militant were killed during a gun battle in the southern village of Mandoora, 35 kilometres (22 miles) south of the main city of Srinagar, said Kashmir's police chief Abdul Gani Mir.

"We launched an operation based on intelligence of the presence of militants in the area," he said.

"One of our boys was martyred in the operation," Mir said, adding that a rebel was also killed and three soldiers were injured.

The incident followed calls by a separatist group for a strike in the region to protest at the weekend shootings. Shops and other businesses, along with schools, were closed and traffic was thin on the streets of Srinagar.

Hundreds of police and paramilitary troops were deployed in the inner parts of the city to try to prevent street demonstrations.

On Sunday soldiers opened fire on angry demonstrators, killing one. The demonstrators had been protesting after the military shot dead a teenager just hours earlier during a hunt for militants.

Police have launched an investigation into the weekend shootings. The army has started its own probe, after describing both incidents as regrettable.

About a dozen armed groups have been fighting Indian forces since 1989 for independence or the merger of the territory with Pakistan.

Kashmir is divided between India and Pakistan by a UN-monitored Line of Control. Both countries claim the Himalayan territory in full.

Tens of thousands of people, mostly civilians, have died in the fighting.