Moana Pasifika management announced this week the Auckland-based franchise would disband at the end of the 2026 season due to financial pressures.
The sport's national federation New Zealand Rugby said on Wednesday there may be potential investors considering taking over the club.
Government agency Sport New Zealand provided funding to help set up Moana Pasifika's entry into Super Rugby in 2022 but Mitchell said the government would not be offering more to prop up the team.
"While there was a good case to support Moana Pasifika in getting established, given the strong Pasifika community in New Zealand and the wider social benefits, that support was always intended to be temporary," Mitchell told New Zealand media.
"The government does not have a role in providing funding for professional sports franchises, and it’s important that any longer-term financial arrangements are worked through independently."
Moana Pasifika's exit will reduce Super Rugby Pacific to a 10-team competition in 2027, and follows the axing of the debt-ridden Melbourne Rebels in 2024.