However, the country rejects all accusations and says its military is fighting against Rohingya, whom the government has termed "terrorists".
The statement called on the Myanmar government to do the same to address the "humanitarian crisis" unfolding in the state.
Besides, dozens of thousands of non-Muslims civilians are reported to have been displaced within Myanmar.
Small solar panels are everywhere in the makeshift refugee camp that has sprouted up to accommodate numerous more than 270,000 people the United Nations says have entered Bangladesh since the violence started. Relatives said she had stepped on a landmine.
"This is a cruel and callous way of adding to the misery of people fleeing a systematic campaign of persecution", she said.
They had escaped before it started, the source said, quoting an eyewitness. As a result, they're effectively stateless.
The latest exodus began on August 25, after Rohingya insurgents attacked police posts in Rakhine, leading to a violent offensive by the Myanmar Army.
A villager said hundreds of Rohingya ran from Pa Din village on Monday after the security forces arrived in the village, fired guns and set houses on fire.
"Amid a dramatic increase in the number of refugees fleeing violence in Myanmar's Northern Rakhine state, UNHCR calls for urgent action to address the root causes of the recent surge in violence, so that people are no longer compelled to flee and can eventually return home in safety and dignity", the statement from the United Nations agency said.
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In a statement, the Ministry of External Affairs (MEA) said that India remains "deeply concerned" about the situation in the Rakhine state and the outflow of refugees from that region.
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However, the spokesman for Myanmar's leader, Aung San Suu Kyi, said on Twitter: "We have no policy to negotiate with terrorists".
Suu Kyi has repeatedly denied accusations of human rights abuses against the Rohingya, and in April denied to the BBC that ethnic cleansing was taking place. The Muslims of Myanmar and Manipur are different, it pointed out.
They have been raped, tortured and killed.
They packed a few precious items into used sacks and bamboo baskets, and then fled on foot through forests, or on precarious boats on rain-swollen rivers.
Anti-Muslim rioting that erupted in Rakhine state in 2012 forced more than 100,000 Rohingya into displacement camps in Bangladesh, where many still live today. They speak their own language, which isn't recognized by the state.
He told the diplomats that some 3,00,000 Rohingya had fled to Bangladesh in the past two weeks, taking the total number of such refugees in the country to over 7,00,000. Rohingya militant groups are often involved in the clashes.