Thousands of people have signed a petition to allow a Ukrainian family denied residency permission to stay in New Zealand.

Nataliya Shchetkova and her husband Alex Derecha arrived here six years ago with three children on a long-term business visa to develop a large restaurant. They also had twins while in New Zealand.

They invested in the La Vista, a popular restaurant in Auckland's St Heliers, and now employ 17 full-time staff - up from nine when they bought it.

But Immigration NZ says the business does not add enough benefit to New Zealand by creating sustained and on-going employment over and above the existing level of employment.

The family of seven have been told they should start planning to leave by July 1 - including selling their restaurant if necessary, RNZ reports.

"We feel like our lives are ruined because we don't understand the reason why," Ms Shchetkova told TVNZ.

"We've worked hard for several years, we contributed to the community."