Aung San Suu Kyi’s long silence over the desperate plight of the Rohingya in Myanmar has been shameful. With tens of thousands now fleeing atrocities in Rakhine state, the Nobel peace prize winner’s aura of moral sanctity lies in tatters. The Muslim minority are denied citizenship by a government which claims, against the evidence, that they are illegal immigrants from Bangladesh. After decades of discrimination, matters got much worse. Since 2012 the Rohingya have endured not just immiseration and the denial of basic rights and services – many live in internment camps – but three major waves of violence by government forces and Buddhist Burman nationalists. Myanmar’s de facto leader has turned a blind eye.

Speak up, people have urged her. Do something. So far her words and actions have been as bad as her reticence. The government has blocked access to United Nations human rights investigators and aid workers. A post on her Facebook page blamed “terrorists” for “a huge iceberg of misinformation” about the current violence. Whether she shares the widespread prejudice towards the Rohingya is a moot question: she does not challenge it. Perhaps the populist Islamophobic forces thriving elsewhere encourage such indifference. On Wednesday, shortly after she met Narendra Modi – no stranger to condoning and exploiting vicious Islamophobia – India’s prime minister said his country shared Myanmar’s concerns about “extremist violence” in Rakhine state.

The Rohingya were already described as the most persecuted people in the world and hundreds of thousands had escaped to Bangladesh, where their conditions are dire. Many have warned of the dangers of radicalisation and attacks on police by a new militant group late last month sparked a wave of violence by government forces. In less than a fortnight, more than 160,000 – from a population of something over 1 million – have fled. Officials say the hundreds who have died in this “clearance operation” are mostly insurgents who have torched Rohingya villages themselves. But there is widespread evidence that the death toll is far higher and most are civilians. Survivors of one massacre told the Guardian of infants and the elderly shot or thrown into the water to drown. Others have spoken of entire families burned alive in their homes. A UN report earlier this year accused security forces of similar crimes. But this violence is on an immense, unprecedented scale.

The UN secretary-general, António Guterres, is pushing hard for concerted action and warns of the risk of ethnic cleansing (several Nobel peace prize laureates say that point has already been reached). But Myanmar has said openly that it is working with China and Russia to prevent a security council rebuke.

Aung San Suu Kyi cannot halt the atrocities at a command. Despite her landslide electoral victory, the military controls key government functions and apparatus on paper as well as in reality – notably security. But a leader who rose to power armed with only her words and moral authority can and should use them in a cause – human rights – which she purported to champion. She is able to shape Burmese public opinion, and to channel it towards curbing the military. A leader who embraced and exploited the support of the international community cannot dismiss its concerns so casually. She is able to press foreign backers to exert more pressure on the armed forces.

Her cloak of virtue has helped to shield them from scrutiny and accountability. The danger is that now her shortcomings will divert attention. The military’s head, Min Aung Hlaing, has no pedestal to topple from. Few even know his name. But they should; he is the man who calls the shots. Finding ways to exert pressure on the military is essential. Suspending the UK’s training of Myanmar’s army would be a good start.

Aung San Suu Kyi has a moral duty to protect the Rohingya. She has ducked it. But she is only a small part of the problem, and of a solution that remains all too distant.