India’s 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 were 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 is 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 mile), poorly drawn Line of Actual Control (LAC) separating the two sides. The LAC is poorly demarcated. The presence of rivers, lakes and snowcaps means the line can shift. The soldiers either side – representing two of the world’s largest armies – come face-to-face at many points.

Border patrols have often bumped into each other, resulting in occasional scuffles.

The last firing on the border happened in 1975 when four Indian soldiers were killed in a remote pass in the north-eastern state of Arunachal Pradesh. The clash was variously described by former diplomats as an ambush and an accident. But no bullets have been fired since.

At the root of this is a 1996 bilateral agreement that says “neither side shall open fire… conduct blast operations or hunt with guns or explosives within two kilometres of the Line of Actual Control”. But there have been tense confrontations along the border in recent weeks. In May Indian and Chinese soldiers exchanged physical blows on the border in the north-eastern Indian state of Sikkim.

India has accused China of sending thousands of troops into Ladakh’s Galwan Valley and says China occupies 38,000 sq km (14,700 sq miles) of its territory. Several rounds of talks in the last three decades have failed to resolve the boundary disputes. The two countries have fought only one war so far, in 1962, when India suffered a humiliating defeat.

There are several reasons why tensions are rising again now – but competing strategic goals lie at the root. The two countries have devoted extensive money and manpower to building roads, bridges, rail links and air fields along the disputed border. Both India and China see each other’s construction efforts as calculated moves to gain a tactical advantage, and tensions often flare up when either announces a major project.

Following the latest clash between China and India, the United Nations urged both sides “to exercise maximum restraint”. “We take positive note of reports that the two countries have engaged to de-escalate the situation,” UN associate spokesperson Eri Kaneko said.

India also disputes part of Kashmir – an ethnically diverse Himalayan region covering about 140,000 sq km – with Pakistan.