The move follows a regional court order for their release that was issue on March 2.
Human rights activists say the UNHCR plans to relocate the 12 Uzbeks in a third country.
Uzbekistan had asked Russia to extradite the 12 -- accusing them of involvement in violence during 2005 in the eastern Uzbek city of Andijon.
Officials been asking for their extradition, accusing them of involvement in the 2005 protest in the eastern Uzbek city of Andijon.