More than 600,000 Rohingya Muslims have fled to Bangladesh since late August, driven out by a military counter-insurgency clearance operation in Buddhist-majority Myanmar's Rakhine State that a top UN official has described as a textbook case of "ethnic cleansing".
"We’re deeply concerned by credible reports of wide-spread atrocities committed by Myanmar’s security forces and by vigilantes who were unrestrained by the security forces during the recent violence in Rakhine State," Tillerson told a joint news conference with Aung San Suu Kyi, the head of a civilian administration that is less than two years old and shares power with the military.
"We’re also distressed by the fact that hundreds of thousands, many women and children have been forced to flee to Bangladesh."
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Tillerson called for a credible and impartial investigation and said those who committed abuses should be held responsible.
“It is incumbent upon the military and security forces to respect these commitments of the civilian government; to assist the government in implementing them and to ensure the safety and security of all people in Rakhine state," Tillerson said.
In posting on his Facebook page, Myanmar's military supremo said he had explained to Tillerson the "true situation in Rakhine", the reasons why Muslims fled, how the military was working with the government to deliver aid and the progress made for a repatriation process to be agreed with Bangladesh.
Tillerson condemned the attacks on Myanmar security forces.
'Staggering'
A senior UN official levelled accusations of mass rape, killings and torture against the Myanmar military, known as the Tatmadaw, after a tour of refugee camps in the Cox's Bazar region of neighbouring Bangladesh.
Human rights groups have branded as a "whitewash" an internal military investigation, after its findings were posted on the army chief's Facebook page this week.
Back in Washington, US senators are pressing for economic sanctions and travel restrictions targeting the Myanmar military and its business interests.
But he said if there was credible and reliable information on abuses by individuals they could be targeted by sanctions.
Myanmar is undergoing a transition to democracy after decades of rule by the military, but the generals retain extensive powers over security and a veto over reform of a constitution that has barred Suu Kyi from the presidency.
Tillerson said the United States would provide an additional $47 million in humanitarian assistance for refugees bringing the total to $87 million since the crisis erupted in August.
"The humanitarian scale of this crisis is staggering. Over 600,000 Rohingya, mostly women and children have fled to Bangladesh and an unknown number from multiple ethnic groups remain internally displaced with limited access to food, water and shelter," Tillerson said.