"We need to support Aung San Suu Kyi and her leadership but also be very clear and unequivocal to the military power sharing in that government that this is unacceptable," Tillerson said.
"This violence must stop. This persecution must stop. It has been characterised by many as ethnic cleansing. That must stop," he said during a visit to London, speaking alongside British counterpart Boris Johnson.
"I think it is a defining moment in many ways for this new emerging democracy," Tillerson said, acknowledging that Myanmar's leader Suu Kyi found herself in a "difficult and complex situation".
Some 389,000 are estimated to have crossed since then.
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