SRINAGAR: A police paramilitary commander was shot dead in Kashmir's main city while at least two suspected separatist militants were killed in gun battles Monday as violence flared in the disputed region on India's Independence Day.

The unnamed commander was critically injured in an ambush and died in hospital, a senior officer of India's Central Reserve Police Force (CRPF) confirmed to AFP, adding that two other members of the force were in a critical condition.

"We have lost a commanding officer. The combing operation is on," said Atul Karwal, the force's inspector general.

Another officer told AFP that two of the attackers are believed to have died in the gunfight in the Nowhatta locality of Srinagar although there would be no confirmation until their bodies were recovered.

CRPF spokesman Bhuvesh Chaudhary said the slain commander was one of nine paramilitaries who were ambushed in two attacks in Nowhatta and there had been another shooting a few kilometres away in the northern part of the city.

India-held Kashmir has been under a curfew since protests broke out over the death last month of the popular young rebel leader Burhan Wani in a gunfight with security forces.

More than 50 civilians have been killed in clashes between protesters and security forces, and thousands more injured in the region's worst violence since 2010.

In a separate gunfight on Monday, two militants were killed near the Line of Control (LoC) in the northern Uri sector, an Indian army spokesman said.

Colonel SD Goswami, a spokesman for the Indian Army, said militants sneaked over onto the Indian side but were challenged by border guards who killed them in a gunfight. Their bodies have been recovered.

Separatist groups traditionally order citizens to observe a shutdown on August 15, India's Independence Day, to protest India rule.

The state's first woman chief minister Mehbooba Mufti called on India and Pakistan to make the LoC irrelevant to bring peace in the region.

"I appeal to both countries that this line dividing Kashmir should be made irrelevant," Mufti told at a thinly attended gathering, after hoisting the Indian flag at a sports stadium in Srinagar.

She blamed the Indian leadership for the current crises in Kashmir and appealed the protesting youth to return to schools and colleges.

Indian Prime Minister Narendra Modi made no direct reference to the situation in Kashmir in his annual Independence Day speech but made a general appeal for an end to violence saying India "will never tolerate terrorism".