There is no "quick fix", Burgener told reporters after briefing the 15 UN Security Council members on the Rohingya refugee situation on Monday.
The special envoy of UN Secretary-General Antonio Guterres said she has "visited many, many people to have an overall picture of the complex situation in Myanmar" since she took office, Xinhua news agency reported.
According to UN refugee agency UNHCR, more than one million ethnic minority Rohingyas have fled their homes in Myanmar's northern Rakhine State since August 2017.
The refugees fled as far as Malaysia and Indonesia, but mainly to neighboring countries, with the overwhelming number going to adjacent Bangladesh, Indo-Asian News Service reported.
During her two trips to Myanmar, Burgener said she worked with Myanmar's State Counselor Aung San Suu Kyi on the Rohingya refugee issue, attended a peace conference, and visited refugee camps, particularly in Cox's Bazar in southern Bangladesh.
Getting the refugees to return home willingly in a safe and dignified manner is a big problem, she said.
While Myanmar's government wants them back, some members of local communities in northern Rakhine State do not.