A Ukrainian family who own a popular Auckland restaurant have received a reprieve from the threat of deportation after the intervention of Associate Immigration Minister Kris Faafoi.

Nataliya Shchetkova, her husband Alex Derecha and their five children are in New Zealand on a entrepreneur visa which runs out on July 1.

The couple, who run La Vista restaurant in St Heliers, have been living on a knife edge after exhausting almost all their options in a bid to stay in New Zealand, which has been their home since 2013.

They renewed their visa twice, the maximum number of times it can be renewed, and applied for residency but it was declined because Immigration NZ said their business did not add significant value to the country.

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An appeal also failed.

The family's last option was to write to Faafoi. A petition signed by 15,000 people also urged Faafoi to intervene and a rally was held for the family.

Shchetkova also appeared before a parliamentary committee to plead their case.

La Vista had a turnover of $1.6 million in the last financial year and employs 26 staff, 17 of them fulltime.

Act leader David Seymour, who has been supporting the family, said today that Faafoi had written to the family to tell them they were allowed to stay for another 12 months which would allow them to apply for residency again.

Shchetkova confirmed the family would reapply for permanent residency.

"I can't say it's a 100 per cent victory but if you compare refusal to a 12-month work visa it is a win," Shchetkova said.

"We want to stay, we're happy to be here and we want to keep doing what we're doing now."

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Shchetkova said she and her husband would not have time to celebrate the good news but her young twins had planned to have a picnic on the beach to mark the occasion.

"We are so happy. My children are going to celebrate; it's the school holidays tomorrow. When I was leaving for work I heard they were arranging to have a picnic tomorrow morning with their school friends."

Seymour said New Zealanders rallied behind the Shchetkovas because they could sense the deep injustice of the situation.

"The family made New Zealand their home six years ago, built a successful business employing 26 people, and now have strong connections in their community. As a country, we must be welcoming of hardworking and entrepreneurial migrants," he said.