"They are regarded as political-asylum seekers, so they have the right to request resettlement in the United States and other countries," Kasit told reporters via tele-conference from Washington.
Kasit discussed the issue with Secretary of State Hillary Clinton during his visit to the US this week.
Australia, Canada, New Zealand and the US have expressed willingness to take eligible political-asylum seekers for resettlement.
Kasit did not say how many the US and others would each be prepared to take, but added that the Foreign Ministry would work this out with the countries' embassies in Bangkok.
However, about 5,000 Hmong in Phetchabun's Ban Huay Nam Khao shelter are not qualified for resettlement since they are normal economic migrants, the minister said.
Thailand and Laos agreed last month to repatriate all of the remaining 5,000 Hmong in Phetchabun by the end of the year, Kasit said.
The two governments will conduct the repatriation programme with transparency to ensure the Hmong can return to their homeland in safety and have good living conditions, he added.
The international community will be able to monitor the returnees. After returning to Laos, they will have the right to ask the Lao government for permission to resettle in other countries, but Thailand will not arrange this for them, Kasit said.
The Hmong in Nong Khai are in a different category. The original group of 147 recognised refugees was rounded up in Bangkok for deportation on November 17, 2006, and was then moved to the Nong Khai Immigration Detention Centre just across the Mekong River from Vientiane on December 8, 2006.
With 11 babies born while their parents have been in detention, their number now stands at 158.
The United Nations High Commissioner for Refugees issued protection for this group as "persons of concern".