Speaking at a joint news conference with leader Aung San Suu Kyi in Myanmar's capital, Tillerson said the US would consider individual sanctions against people found responsible for the violence, but he would not advise "broad-based economic sanctions" against the entire country.
A Myanmar military report that said no Rohingya civilians were killed during a months-long crackdown is "absurd" and the International Criminal Court must now launch its own investigtion, a human rights group said.
While the report acknowledged that battles against militants from the Arakan Rohingya Salvation Army, or ARSA, had left 376 "terrorists" dead, it also claimed security forces had "never shot at the innocent Bengalis" and "there was no death of innocent people".
Also on Wednesday, Tillerson is expected to tell Senior General Min Aung Hlaing, commander-in-chief of Myanmar's armed forces, to end the violence in Rakhine to prevent Rohingya Muslims from fleeing to Bangladesh, Reuters reported, citing a U.S. State Department diplomat.
This violence has displaced almost a million Rohingya civilians from their homes, almost 700,000 of whom have left Myanmar altogether to seek refuge in Bangladesh.
"Secretary Tillerson's visit must be used to recognize the tragedy for what it is, ethnic cleansing, and to pressure the Myanmar government and in particular Myanmar's military to address the crimes against humanity that are taking place", said Eric Schwartz, president of Refugees International, in a statement.
Since Aug. 25 more than 617,000 Rohingya refugees have arrived in Cox's Bazar, Bangladesh, fleeing violence in Myanmar, Millman said.
While world leaders wrung their hands, thousands of Rohingya remained stranded in Burma, on beaches around the mouth of the Naf River, hoping to find a boat to make the short, sometimes perilous crossing to Bangladesh.
With fewer boats available, desperate Rohingya have been stringing together rafts from bamboo and plastic canisters.
"They're still coming, risking their lives, driven by fears of starvation and violence", Shariful Azam, a police official in Bangladesh's Cox's Bazar, a narrow spit of land where the world's most urgent humanitarian crisis is unfolding.
On Friday, the Burmese military replaced the commanding officer in Rakhine State. It is widely believed among the Buddhist-majority population that Rohingya are "illegal immigrants" from Bangladesh, despite having resided in Burma for hundreds of years. Stressing the importance of holding to account those responsible for human rights abuses and violations, the Security Council statement called for the Government of Myanmar to co-operate with the UN High Commissioner for Human Rights.
"After recording countless stories of horror and using satellite analysis to track the growing devastation we can only reach one conclusion: These attacks amount to crimes against humanity".
On Monday, British Prime Minister Theresa May's spokesman stated that the crisis in Myanmar "looks like ethnic cleansing".
Myanmar's military has denied the accusations, most recently with a statement Monday.
"And it is something for which the Burmese authorities - and especially the military - must take full responsibility".
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