Officials from the city of St Paul, Minnesota, began talks on Monday to finalise reception for thousands who fled communist Laos to find shelter in a Thai temple.
But Mayor Randy Kelly's monogamy clause has turned out to be a big problem.
General Pallop Pinmanee, of Thailand's Internal Security Operations Command has said he will meet with Kelly to discuss the only-one-wife condition.
"Many Hmongs have several wives. How can we separate family members?"
Pallop said a further "problem is there are about 1000 senior Hmongs who don't want to go to the US. They want to stay at Tham Krabok which we can not allow."
Tham Krabok, a Buddhist temple in central Thailand, houses about 14,400 refugees who were recently accepted for entry into the United States. More than half are destined for St Paul.
A 20-member US delegation is scheduled to visit the camp on Tuesday, where residents are already undergoing tests to prove they are in good health and not addicted to drugs.
"There are about 1000 senior Hmongs who don't want to go to the US. They want to stay at Tham Krabok which we can not allow"
General Pallop Pinmanee, Thailand's Internal Security Operations Command
A US embassy official said discussions were going well, but the delegation was now settling down to the "nitty gritty" of the resettlement process.
Why the US?
Minnesota has taken in tens of thousands of Hmong refugees in recognition of their help to US forces during the Vietnam war and the minority's subsequent persecution.
The Hmong at Tham Krabok are among the last of 300,000 who fled to Thailand after the communist takeover in Laos in 1975.
Their presence has long been a thorny issue between Vientiane and Bangkok.