The agency says the refugees traveled from the crowded Mae La camp in northern Thailand to Bangkok, where they will fly to the United States.
An official with the UN agency, Hasim Utkan, says the refugees have little realistic prospect of going home and have been leading what he called a very restricted life in the Thai camp for more than a decade.
The agency is planning for nearly 10,000 Burmese refugees from Thailand to emigrate to the United States by the end of September. Most of the refugees are from the Mae La camp.
Some 45,000 mainly ethnic Karen refugees live in Mae La, one of nine refugee camps run by the Thai government along the border with Burma.
Information for this story is provided by UNHCR.