The spokesman for Myanmar's leader Aung San Suu Kyi, however, said on Twitter: "We have no policy to negotiate with terrorists".
"We are on the brink of witnessing another Rwanda or Srebenica", said Raees Ahmed, a Rohingya Muslim with family members stuck in the country.
The brutal repression of Myanmar's Muslim Rohingya minority by state security forces has sparked a massive refugee crisis in recent weeks but so far has elicited little response from the United States.
Myanmar's army says at least 400 people, mainly militants, have been killed in the violence.
The Organisation of Islamic Cooperation (OIC) on Sunday condemned Myanmar for "systematic brutal acts" against its Muslim Rohingya minority and asked it to accept worldwide monitors. Myanmar has one of the few militaries that use anti-personnel mines, which were banned under an worldwide treaty in 1997.
Rumours have spread on social media that Muslims, who represent about 4.3 per cent of the Buddhist-majority country's population of 51.4 million, would stage attacks on September 11 to avenge violence against the Rohingya in northern Rakhine. Hafez Ahmed, 60, told AFP.
Suu Kyi, a Nobel peace laureate, has come in for strong worldwide criticism over the military crackdown on the Rohingya, which began when militants ambushed security forces on August 25.
The first ARSA attacks in October a year ago were less ambitious, but the subsequent military response by a security force notorious for its scorched earth response to insurgency sent 90,000 Rohingya fleeing across the border.
"Otherwise, the massacre and butchering will continue to happen".
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Rohingya have faced decades of discrimination and persecution in Burma and are denied citizenship despite centuries-old roots in the Rakhine region.
"The UN and INGOs have not been very welcome in Rakhine and...they are not able to operate and ensure the safety and security of their staff and volunteers", said Joy Singhal of the International Federation of Red Cross and Red Crescent Societies (IFRC).
"She lost her houses and properties".
But there several cases that point to anti-personnel land mines or other explosives as the cause of injuries on the border with Bangladesh.
Those still waiting to cross into Bangladesh - many hungry and exhausted after a days-long march through the mountains and bushes in monsoon rain - have been stopped because of a crackdown on Bangladeshi boatmen charging 10,000 taka ($122) or more per person, sources said.
"Myanmar can take back its citizens after ascertaining their nationality through verifications". "And yet the Prime Minister has not acted in a forceful and decisive manner", said Khan, who has also crafted an online petition calling for the same thing.
Some have called for the Nobel Peace Prize Suu Kyi won in 1991 as a champion of democracy to be revoked.
The statement called on the Myanmar government to do the same.
REUTERS/Mohammad Ponir HossainRohingya refugees walk to the shore with his belongings after crossing the Bangladesh-Myanmar border by boat through the Bay of Bengal in Teknaf, Bangladesh.