I would expect that the leader of the country would be able to contain it, and would be able to reverse the situation," Guterres said in an interview with the BBC.
"She has a chance, she has a last chance, in my opinion, to do so."
He warned that "the tragedy will be absolutely horrible," if Suu Kyi and the influential Myanmar military do not solve the crisis soon.
The number of the Muslim Rohinyga refugees in Bangladesh has topped 410,000, according to the UN Children's Fund (UNICEF). Thousands more arrive every day, the UN said on Sunday.