There is no Rohingya amongst Myanmar's ethnicities. The UN should send a fact-finding mission to Rakhine State and persuade the Myanmar Government to allow necessary humanitarian access for the Rohingya Muslim population.
Talking to reporters here, Tillerson also likened the violence against Myanmar's Rohingya Muslims to ethnic cleansing.
The Southeast Asian nation's first civilian leader in decades has faced global condemnation for a lack of moral leadership regarding the Rohingya, victims of what the UN views as a campaign of ethnic cleansing.
"In my view, publicly condemning Aung San Suu Kyi, the best hope for democratic reform in Burma, is not constructive" and could slow the progress toward a representative government, McConnell said.
Attacks by Rohingya militants on security posts last month triggered an army operation that has killed more than 400 people, destroyed over 6,800 houses and sent almost 400,000 Rohingya Muslims fleeing to Bangladesh.
Earlier on Thursday the European Parliament passed a resolution calling on the "military and security forces in Myanmar to immediately cease the killings, harassment, and rape of the Rohingya people, and the burning of their homes".
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.
Meanwhile, UN Secretary-General Antonio Guterres, Wednesday called on Myanmar to halt military action and atrocities against the Rohingya in Rakhine state, saying the ongoing violence by security forces against the Muslim minority was "completely unacceptable and catastrophic".
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.
One of the dozens of boats carrying Rohingya to the Bangladeshi border town of Teknaf capsized on Thursday and at least two people drowned, police said. Observers say the violence is being carried out by the Burmese military. According to Bangladesh, around 3,000 Rohingya have been killed in the crackdown.