The treatment of Myanmar's Rohingya is the biggest challenge facing national leader Aung San Suu Kyi, accused by some Western critics of not speaking out for a minority that has long complained of persecution.
An estimated 2,000 Rohingya were believed to have made it across the border overnight.
Thousands of ethnic Rakhine Buddhists and other local ethnic groups have also been displaced - the apparent targets of militants who are fighting under the banner of the Arakan Rohingya Salvation Army (ARSA).
"The secretary-general is deeply concerned by the reports of excesses during the security operations conducted by Myanmar's security forces in Rakhine State and urges restraint and calm to avoid a humanitarian catastrophe", said a United Nations spokesman. It said the locations match some of the accounts given by people who have fled into Bangladesh of settlements that have been attacked and destroyed by Myanmar soldiers, police and armed civilians.
Sham Shu Hoque, 34, crossed the border with 17 family members.
In the wake of the report, Aung San Suu Kyi has accused worldwide aid workers of helping "terrorists" in the region.
Some Rohingya people with bullet and burn injuries have been admitted to different hospitals in the last three days.
"Many children have been killed", he told BuzzFeed News from Geneva, "many women, many elderly". In 2009, a United Nations spokeswoman even described the Rohingya as "probably the most friendless people in the world".
A group of Rohingya refugees takes shelter at the Kutuupalang makeshift refugee camp in Cox's Bazar in Bangladesh.
"On the other side, another harsh military response and the continued displacement of scores of thousands to camps in Bangladesh will create conditions ripe for exploitation by transnational jihadists". Bangladesh's unwillingness to host more refugees became apparent in the government's plan to relocate Rohingyas to a remote island that is mostly flooded during the monsoon season.
The situation in Rakhine is a "matter of great concern", a senior MEA official said on Friday, adding, "A large number of people have lost their lives".
"As Burmese security forces act to prevent further violence, they have a responsibility to adhere to global humanitarian law, which includes refraining from attacking innocent civilians and humanitarian workers and ensuring assistance reaches those in need", Haley said.
Numerous new arrivals were women and children, including heavily pregnant women, she said. "They also seem traumatized by what they have been through", Tan told DW.
Rohingya are reviled in Myanmar as illegal immigrants and roughly one million have been denied citizenship. It noted a similar phenomenon from October to November 2016, the last time major violence flared in the region, triggering an exodus of some 87,000 Rohingya refugees to Bangladesh.
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