A US delegation has visited ethnic Hmong refugees in Thailand, ahead of their resettlement in the US.
The US says it feels a special responsibility to the Hmong
Delegation leader Randy Kelly described the Hmong camp as "desolate" and promised its inhabitants a better life.
Up to 15,000 refugees in Thailand's Wat Tham Krabok camp could be eligible for the resettlement programme.
Large numbers of Hmong have been homeless since they supported the US army when the Vietnam War spread to Laos, then fled the communist takeover.
Mr Kelly, mayor of St Paul, Minnesota, one of the largest communities of Hmong in the US, said it was a "powerful moment" to meet the camp's inhabitants.
"I assured them (the Hmong) that when they come to the US, if they work hard and continue to have a value in education they could become successful. I tried to provide them the hope of a better future," he said.
Thai officials said they had raised the delicate issue of polygamy with the visitors.
Polygamy is widespread among Hmong but is illegal in the US.
Pallor Pentane, deputy head of Thailand's Internal Security Operations Command which oversees the camp, said he was concerned after receiving reports that at least one US state would limit men to one spouse only.
"I told them that this would be against human rights," he told Reuters news agency, adding that the US delegation appeared sympathetic to the issue.
M Kelly told reporters that he could not comment on the issue, which would be debated "at a much higher level".
However, Anthony Newman of the International Organisation for Migration (IOM) said that in practise the issue was negotiable.
"On paper, they can have one wife only. But in reality they can all move together to the United States and stay together as a family group," he said.
The resettlement process will take about three months for each applicant, with Department of Homeland Security interviews beginning in May, IOM physicals in June and resettlement to the US beginning in August.
Based near Sara Uri, 130 km (80 miles) north of Bangkok, Wat Tham Krabok is the only official refugee centre in Thailand for Hmong refugees, and is regarded by the Thai authorities as a base for rebel activities.
During the Vietnam War large numbers of ethnic Hmong sided with the US army as the conflict spread into neighbouring Laos, and played an important support role.
But at the end of the war, the US Government stopped its support for the Hmong. When a communist movement ousted the US-backed Lao royal family in 1975, as many as a third of the Hmong population are thought to have fled.