New figures show around 21,000 Rohingya Muslims have fled Burma in recent weeks amid accusations of potential “genocide”.

The International Organisation for Migration (IOM) said: “An estimated 21,000 Rohingya have arrived in Cox's Bazar between 9 October and 2 December.”

The government of Burma has criticised media reports of violence against the Rohingya, and lodged a formal protest against a UN official in Bangladesh who said the state was carrying out “ethnic cleansing”.

At the weekend, the Malaysian Prime Minister Najib Razak led a protest rally against what he called the “genocide” of the Rohingya minority, saying “enough is enough”. 

Malaysia's prime minister leads protest against 'genocide'

And the UN’s rights agency has said the Rohingya may be victims of “crimes against humanity”, and that Burma “has largely failed to act on the recommendations made in a report by the UN Human Rights Office”.

Burma does not allow foreign journalists and investigators access to the western Rakhine province where the worst abuses are alleged to have taken place.

But refugees interviewed in Bangladesh relayed allegations of gang rape, torture and murder at the hands of state security forces, according to the AFP news agency.

An analysis of satellite images by Human Rights Watch found hundreds of buildings in Rohingya villages have been razed.

The conflict stems from a breakdown in relations between Burma’s Theravada Buddhists and the Rohingya, a Muslim minority group, that has resulted in one of the worst refugee crises in the world.

The election victory of Burma's Nobel peace laureate and now de facto leader Aung San Suu Kyi spawned hopes that the government would act to foster a safer environment for the Rohingya, and last week she vowed to work for “peace and national reconciliation”. 

In practice, though, the country’s military has retained control of all aspects of state leadership that relate in any way to “security”, and that includes policy towards the Rohingya. 

Former UN chief Kofi Annan, during a vist to the country on Tuesday, urged Burma's security forces to act within the rule of law in the country's northwest, where the army crackdown that has killed at least 86 people. Security forces poured into the area following a series of attacks on police posts in recent weeks that authorities have blamed on local militants.

Security operations must not compromise citizens' civil rights, said Mr Annan, who heads a government-appointed panel tasked with finding solutions to the conflict between Burma's Buddhists and the Muslim Rohingyas.

“There is no trade-off between security and civil liberties,” he said, after meeting state counsellor Ms Suu Kyi and commander-in-chief Min Aung Hlaing on his second visit to the country.

“Wherever security operations might be necessary, civilians must be protected at all times and I urge the security services to act in full compliance with the rule of law.”

The committee was “deeply concerned by reports of alleged human rights abuses”, Mr Annan said.

Ms Suu Kyi appointed the nine-member panel before the current fighting erupted to advise on the restive state, where ethnic Rakhine Buddhists and the Rohingya Muslims have lived separately since clashes in 2012 that killed more than 100 people.

Burma's authorities have rejected allegations by residents and rights groups that soldiers raped Rohingya women, burnt homes and killed civilians during a crackdown in response to the coordinated attacks on three border posts along the frontier with Bangladesh. Ms Suu Kyi has pledged an investigation into the current violence.

Bangladesh has also proved reluctant to accept the Rohingya people, resisting calls to open its borders to the half a million still inside Burma and increasing border patrols.

Islam is by far the majority religion in Bangladesh, and there has been outrage in the country at the treatment of their fellow Muslims across the border.

On Tuesday police stopped thousands of hardline Muslims from marching to the Myanmar embassy in Dhaka to protest at the ongoing “genocide” of Rohingya.

Shiblee Noman, an assistant commissioner of Dhaka police, told AFP about 10,000 Muslims joined the march, which was halted at central Dhaka's Nightingale Crossing.

“They were peaceful,” he said.

More than 230,000 Rohingya are already living in Bangladesh, most of them illegally, although around 32,000 are formally registered as refugees.