NEW DELHI — The worst border clash between India and China in more than 40 years left 20 Indian soldiers dead and dozens believed captured, Indian officials said Tuesday, raising tensions between nuclear-armed rivals who have increasingly been flexing their diplomatic and military muscle.

For the past several weeks, after a series of brawls along their disputed border, China and India have been building up their forces in the remote Galwan Valley, high up in the Himalayas.

As they dug into opposing positions, adding tinder to a long-smoldering conflict, China took an especially muscular posture, sending in artillery, armored personnel carriers, dump trucks and excavators. On Monday night, a huge fight broke out between Chinese and Indian troops in roughly the same barren area where these two nations, the world’s most populous, had fought a war in 1962.

Military and political analysts say the two countries do not want a further escalation — particularly India, where military forces are nowhere near as powerful as China’s — but they may struggle to find a way out of the conflict that does not hint at backing down.

Both countries and their nationalist leaders, President Xi Jinping of China and Prime Minister Narendra Modi of India, have taken increasingly assertive postures that pose real risks of conflict spinning out of control.

“Neither PM Modi or President Xi want a war, but neither can relinquish their territorial claims either,” said Ashley J. Tellis, a senior fellow at the Carnegie Endowment for International Peace in Washington.

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What’s happening along the Himalayan border is an unusual kind of warfare. As in the brawls last month, Chinese and Indian soldiers fought fiercely without firing a shot — at least that’s what officials on both sides contend. They say the soldiers followed their de facto border code not to use firearms and went at each other with fists, rocks and wooden clubs, some possibly studded with nails or wrapped in barbed wire.

At first, India’s military said only three Indian troops had been killed in the clash, where the Ladakh region of India abuts Aksai Chin, an area controlled by China but claimed by both countries. But late Tuesday night, a military spokesman said that 17 other Indian soldiers had succumbed to injuries sustained in the clash, bringing the total dead to 20.

An Indian commander said dozens of soldiers were missing, apparently captured by the Chinese. Indian television channels reported that several Chinese soldiers had been killed as well, citing high-level Indian government sources. Chinese officials did not comment on that.

It’s not clear what India can do now. Modi and his Hindu nationalist party have pursued a forceful foreign policy that emphasizes India’s growing role in the world, and last year, after a devastating suicide attack that India blamed on a Pakistani terror group, Modi ordered airstrikes on Pakistan, bringing the two countries to the brink of war. But India is in no shape to risk a war against China — especially now, as it slips deeper into the economic and health crisis caused by the coronavirus, which has cost the country more than 100 million jobs.

“Whatever India might want to do it’s not in a position to do,” said Bharat Karnad, a professor of security studies at the Center for Policy Research at New Delhi.

“The Modi government is in a difficult position,” he said. “This is bound to escalate.”

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And, he added, “we are not prepared for this kind of escalation.”

Xi has been doubling down on China’s territorial claims across Asia, backing up arguments with the threat of force or sometimes even the use of force. In recent weeks, the Chinese have tightened their grip on the semiautonomous region of Hong Kong; menaced Taiwan; and sunk a Vietnamese fishing boat in the South China Sea.

The upshot, scholars say, is a dangerous break from the past. China and India, with their growing ambitions and growing militaries are increasingly bumping up against each other along their 2,100-mile border.

“Over the past several decades there’s been incessant confrontation between China and India, but proudly there have been no shots fired or deaths,” said Long Xingchun, a professor at China West Normal University in southwest China who studies relations with India. But now, he added, neither side is as willing to compromise, raising the risks of more fighting, even if the countries don’t actually want to go to war.

“There was no reason for this to happen,” he said. “Unless it was a military standoff that got out of control.”

The State Department in Washington said the United States was “closely monitoring” the dispute. “Both India and China have expressed a desire to de-escalate, and we support a peaceful resolution of the current situation,” the department said in a statement.

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It’s difficult to know the exact trigger or severity of the fighting. The Galwan Valley is a rocky, icy, inhospitable slice of the Himalayas, off-limits to all but a few lonely herdsmen and Indian and Chinese troops. Each side was quick to blame the other for violence along the Line of Actual Control, the boundary that emerged from the 1962 war.

“The Indian military broke their promises and once again crossed the Line of Actual Control to engage in illegal activities,” Col. Zhang Shuili, a Chinese military spokesman, said in a statement. “They deliberately launched a provocative assault, leading to an intense physical clash that caused death and injury.”

An Indian military official said the clash started during a meeting attended by hundreds of soldiers on both sides who had come together along the border to discuss efforts to de-escalate tensions. For the past week, Indian military officials had been reassuring the Indian public that the border was calming down and that they were having productive talks with the Chinese, through diplomatic and military channels.

But, according to the Indians, Chinese officers insulted them at the meeting Monday night, which triggered a fight between soldiers that quickly spiraled into a major melee.

“A violent faceoff happened as a result of an attempt by the Chinese side to unilaterally change the status quo,” said a statement from Anurag Srivastava, an Indian government spokesman. “Both sides suffered casualties that could have been avoided had the agreement at the higher level been scrupulously followed by the Chinese side.”

China and India said Tuesday they were committed to resolving their differences through dialogue, but again, it wasn’t clear if the military commanders along the border were standing down or gearing up.

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Also, if brawls in May were any indication, the casualties from Monday may end up higher than reported. The clashes in May, which erupted at several border points, were first reported as minor. Only weeks later was it revealed that Chinese and Indian soldiers had been briefly captured and some beaten so badly they required airlifting to hospitals hundreds of miles away.

Both countries run patrols along the disputed border, and the soldiers are under strict orders not to shoot, but that doesn’t stop them from throwing rocks. Or fighting with crude weapons.

“This was an incident waiting to happen,” said H.S. Panag, a retired Indian general, of the latest fighting.

The surge in violence is a product of the protracted dispute between India and China over the precise location of their jagged Himalayan border, which cuts through a desolate landscape home to few people or resources that would be easy to extract. Both sides maintain high-elevation military installations facing each other, and armed skirmishes continued through the late 1960s and mid-70s.

The spark for the recent tensions seemed to have been a road to a remote air force base that the Indian army is building through the Galwan Valley. Military analysts say that the road is fully within Indian territory but that the Chinese are determined to frustrate India’s efforts to upgrade its military positions.

And the wider backdrop is that India and China have been competing for influence on many fronts across South Asia.

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Several countries, such as Nepal and Sri Lanka, that were once reliable Indian allies have recently tilted toward China, wooed by Chinese investment. And Pakistan, India’s archenemy, is now fully aligned with China, working hand in hand with the Chinese military.

But that doesn’t necessarily mean that the China-India relationship will worsen. Modi and Xi have held several friendly meetings.

And last year China helped Modi during his reelection campaign by agreeing to a United Nations resolution that designated Masood Azhar, a Pakistani militant, as a global terrorist. China had refused to do this for a long time, but after determined lobbying by India and others, China relented, handing Modi a diplomatic victory at a crucial time.

But then India did something that aggravated China. A few months later, after Modi won a landslide election, his home minister, Amit Shah, vowed to take back Aksai Chin. During a speech in Parliament about the disputed region of Kashmir, Shah said that Aksai Chin and all of Kashmir belonged to India and India would “sacrifice life for this.”

Analysts say the Aksai Chin issue, along with India’s warming relations with the United States, have become irritants to China, which may now be using its military to harass India as payback.