(CNN) More than a quarter of a million Rohingya refugees have flooded into Bangladesh in just two weeks, fleeing violence in Myanmar's Rakhine state, the United Nations refugee agency said Friday.

Spokesman William Spindler said 270,000 Rohingya had crossed the border since August 25, when clashes between the military and militants intensified.

The new numbers represent roughly a third of the country's Rohingya people, a stateless Muslim minority, although the Myanmar government doesn't release exact population figures.

Yanghee Lee, the United Nations Special Rapporteur on Human Rights for Myanmar, said Friday that at least 1,000 people had been killed in the violence over the past two weeks, though she said that figure is "very likely an underestimate."

"Figures are difficult to verify because of lack of access to the affected areas," she said.

The Myanmar government said 421 people had died.

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The Rohingya are considered to be among the world's most persecuted people. The predominantly Buddhist Myanmar considers them Bangladeshi but Bangladesh says they're Burmese.

The government of Myanmar, formerly known as Burma, blames terrorists for starting the recent violence.

Rohingya militants killed 12 security officers in border post attacks almost two weeks ago, according to state media.

Children, women drown while fleeing

Not all of the refugees are making it to Bangladesh safely.

Dozens of Rohingya women and children fleeing the violence have drowned while attempting to escape to Bangladesh by boat.

A Bangladeshi border guard, who asked not to be identified, told CNN guards had retrieved eight bodies on the Bangladeshi side of the Naf River on Wednesday alone, half of whom were children.

"It was a case of a boat capsizing," he said. " (But) this has been happening from day one ... Since then, around 60 to 65 bodies have arrived south (of the border area.) In other areas, maybe 10 to 15."

Rohingya Muslim refugees make their way into Bangladesh after crossing the border on September 7.

The border guard sent CNN photos appearing to show young children lying dead on the banks of the Naf River.

"No-one comes to collect these bodies. These people are so distressed, they are walking, coming across fields for five days, they hardly recognize their own relatives," he said.

The border guard said some Rohingya have been paying fishermen as much as $250 per person to ferry them across the river on "very risky" boats.

"They are not designed to travel on this rough sea, they are taking long detour. It's not only the type of boat, it is the capacity, only made for five, six, or 10 people and they are taking double or triple that number sometimes," he said.

Rohingya Muslim refugees make their way into Bangladesh after crossing the border on September 07.

Desmond Tutu begs Suu Kyi to help

As the humanitarian crisis in South Asia continued to grow, Archbishop Emeritus Desmond Tutu wrote to his fellow Nobel laureate Aung San Suu Kyi, begging her to stop the violence.

"I am ... breaking my vow of silence on public affairs out of profound sadness about the plight of the Muslim minority in your country, the Rohingya," he wrote in an open letter, posted on his official Twitter.

As we witness the unfolding horror we pray for you to be courageous & resilient again. #Rohingya #PrayForRohingya pic.twitter.com/BIDSYY9e1X — DesmondTutu Official (@TheDesmondTutu) September 7, 2017

In his letter, Tutu described Suu Kyi as "a beloved younger sister," and how he used to keep a photo of her on his desk to remind him of the woman who symbolized "righteousness" in the world.

"But what some have called 'ethnic cleansing' and others 'a slow genocide' has persisted -- and recently accelerated. The images we are seeing of the suffering of the Rohingya fill us with pain and dread," he said.

The former archbishop said any country which was "not at peace with itself" was not a free country. "If the political price of your ascension to the highest office in Myanmar is your silence, the price is surely too steep," he said.

Tutu is the second Nobel laureate to strongly condemn Suu Kyi for her inaction. Malala Yousafzai, the youngest recipient of the prize, said "the world was waiting" for the Myanmar leader to help the refugees.

Outrage grows in Bangladesh

As refugees continue to pour across the border, discontent is growing inside Bangladesh at the ongoing violence in their neighboring Rakhine State.

A protest in the capital Dhaka took place on Friday , while other demonstrations in support of the Rohingya were also held in Pakistan, Indonesia and the Philippines.

The Bangladeshi government summoned the Myanmar ambassador Wednesday to raise concerns about reports of landmines being laid on the border in the path of refugees.

There have been reports of Rohingya being crippled after stepping on the hidden mines while making their way to safety across the border.

"It's possible the Myanmar military has planted the mines. There is no one else who could do it," a senior Bangladeshi border guard told CNN.

Myanmar state media blamed local "terrorists" for placing mines in Rakhine State -- where Rohingyas are concentrated -- although not specifically on the border.