The Indian prime minister has made his first comments about the killing of at least 20 soldiers in a clash with Chinese troops in a disputed Himalayan border area. In a televised address about Monday’s violence, Narendra Modi warned the deaths “will not be in vain”.

Soldiers reportedly brawled with sticks, bats, and bamboo sticks studded with nails in the Ladakh region. Both sides insist no shots were fired, as part of a longstanding pact. India’s army said China also suffered casualties but Beijing has given no details.

The Indian statement notes that injured soldiers were “exposed to sub-zero temperatures in the high altitude terrain”.

It is the first deadly clash between the two sides in the border area, in the disputed Kashmir region, in at least 45 years. India said China had tried to “unilaterally change the status quo”. Beijing accused Indian troops of “attacking Chinese personnel”. The two armies later held talks to try to defuse tensions.

The fighting occurred in the precipitous, rocky terrain of the strategically important Galwan Valley, which lies between China’s Tibet and India’s Ladakh. Indian media say soldiers engaged in direct hand-to-hand combat, with some “beaten to death”. During the fight, one newspaper reported, others fell or were pushed into a river.

The Indian Army initially said a colonel and two soldiers had died. It later said that “17 Indian troops who were critically injured in the line of duty” and died from their injuries, taking the “total that was killed in action to 20”. The clash has provoked protests in India, with people burning Chinese flags.

Addressing the issue on Wednesday, Prime Minister Modi said: “India wants peace but when provoked, India is capable of giving a fitting reply, be it any kind of situation. He said he wanted to “assure the nation” the loss of the soldiers would “not be in vain”. “For us, the unity and sovereignty of the country are the most important,” he added.

China did not confirm the number of casualties but accused India of crossing the border onto the Chinese side.

China’s foreign ministry said on Wednesday it wanted to avoid further clashes and reiterated that it was not to blame. This is not the first time the two nuclear-armed neighbours have fought without conventional firearms on the border.

India and China have a history of face-offs and overlapping territorial claims along the more than 3,440km (2,100 miles), poorly drawn Line of Actual Control (LAC) separating the two sides.