Relations have plunged to their lowest level in years, with India accusing Pakistan of supporting "cross-border terrorism" after gunmen carried out the worst attack on civilians in contested Muslim-majority Kashmir for a quarter of a century.

Syed Ashfaq Gilani, a government official in Pakistan-administered Kashmir, told AFP Friday that troops exchanged fire along the Line of Control (LOC) that separates the two countries.

"There was no firing on the civilian population," he added.

India's army confirmed there had been limited firing of small arms that it said had been "initiated by Pakistan", adding it had been "effectively responded to".

On Thursday, UN spokesman Stephane Dujarric told reporters in New York that issues between the countries "can be and should be resolved peacefully through meaningful mutual engagement".

"We very much appeal to both the governments... to exercise maximum restraint, and to ensure that the situation and the developments we've seen do not deteriorate any further," he said.

Indian Prime Minister Narendra Modi has vowed to hunt down the gunmen responsible for killing 26 civilians at the popular tourist site of Pahalgam, after Indian police identified two of the three fugitive gunmen as Pakistani.

"I say to the whole world: India will identify, track and punish every terrorist and their backer," Modi said, in his first speech since Tuesday's attack in the Himalayan region.

"We will pursue them to the ends of the Earth."

Denying any involvement, Islamabad called attempts to link Pakistan to the Pahalgam attack "frivolous" and vowed to respond to any Indian action.

"Any threat to Pakistan's sovereignty and to the security of its people will be met with firm reciprocal measures in all domains," a statement said, after Prime Minister Shehbaz Sharif held a rare National Security Committee with top military chiefs.

Kashmir has been divided between India and Pakistan since their independence in 1947, with both claiming the territory in full but governing separate portions of it.

Rebel groups have waged an insurgency in Indian-controlled Kashmir since 1989, demanding independence or a merger with Pakistan.

India's air force and navy both carried out military exercises Thursday.

Indian police say the three gunmen are members of the Pakistan-based Lashkar-e-Taiba group, a UN-designated terrorist organisation. 

They offered a two million rupee ($23,500) bounty for information leading to each man's arrest.

A day after the attack, New Delhi suspended a water-sharing treaty, announced the closure of the main land border crossing with Pakistan, downgraded diplomatic ties, and withdrew visas for Pakistanis.

In response, Islamabad on Thursday ordered the expulsion of Indian diplomats and military advisers, cancelling visas for Indian nationals -- with the exception of Sikh pilgrims -- and closing the main border crossing from its side.

Pakistan also warned any attempt by India to stop the supply of water from the Indus River would be an "act of war."