But the former political prisoner has faced growing criticism from fellow Nobel laureates over her response to what the United Nations human rights chief called a "textbook example of ethnic cleansing".
The Rohingya, described by the United Nations as among the world's most persecuted peoples, have faced heightened fears of attack since dozens were killed in communal violence in 2012.
Tillerson said the USA appreciated the "difficult and complex situation" Suu Kyi finds herself in, sharing political power with the military, but he also described the "horrors" occurring in the Southeast Asian nation as a "defining moment" for its new democracy.
The US Secretary of State, Rex Tillerson, has called the crisis a "defining moment" for Myanmar and its de facto leader, Aung San Suu Kyi.
In a Facebook post, Dr Balakrishnan said he had a "warm and open discussion" with Aung San Suu Kyi on the situation in Rakhine State. Based on its analysis of video, satellite photos, witness accounts and other data, the human rights group said more than 80 inhabited sites, each at least 375 meters (1,230 feet) in length, have been torched in strife-hit Rakhine State.
McConnell, whose Republicans control majorities in both houses of Congress, repeated earlier criticism of a resolution introduced in the US Senate urging Suu Kyi to do more for Myanmar's ethnic minority Rohingya population, and lessening the chance that any such measure could pass. "In legal terms, these are crimes against humanity".
"Violence in Myanmar has created a humanitarian catastrophe".
McConnell has had close ties to Suu Kyi for years.
At a press conference late Wednesday, government spokesman Zaw Htay announced Suu Kyi will address citizens next week with a message of peace and national reconciliation. He warned that weakening her could interfere with the country's transition from decades of military rule.
Aung San Suu Kyi's attends a Myanmar parliament meeting on April 8, 2015. "And attacking the single political leader who has worked to further democracy within Burma is likely to hinder the objective over the long run", McConnell concluded.
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