The family of an Auckland couple ordered to leave New Zealand for overstaying their visas are in turmoil this morning. Loasi Latu and her husband have lived in New Zealand for decades, but have overstayed their visas by more than 20 years. They were told they needed to leave the country by last Friday but did not, believing a ministerial intervention was possible. But Associate Immigration Minister Chris Penk says he won't intervene, and he has asked Immigration officials to make contact with the family today to clarify what happens next. Mr Penk declined to be interviewed by Morning Report, but in a statement he said: “I acknowledge this is a difficult situation for Loasi Latu, her husband, and their family. However, for privacy reasons I cannot comment on specific details related to individual cases. "Immigration matters such as these are complex and involve balancing a range of factors. Many people every year are declined immigration status in New Zealand and while it is disappointing for the individuals concerned, to protect the integrity of our immigration system, it’s important that we have a consistent and robust process for evaluating applications.  "A voluntary departure does not preclude people returning to New Zealand if they are able to obtain the necessary visa, but this will depend on the individual’s circumstances. This is now an operational matter for Immigration New Zealand.” In a statement, the Latu family said it is still waiting to hear from the Minister. "The Associate Immigration Minister, Chris Penk, hasn't come forward to speak to us yet," the statement said.  "We already feel that New Zealand is behind us. Even the Prime Minister said in his Monday press conference that our situation is heartbreaking.  "It would be very hurtful if Mr Penk's commentary is in fact true, and he has reduced the seriousness of our case to an 'operational issue.' "Even more heartbreaking would be that they have told media before telling our family." The Green Party has thrown its support behind the family, urging the Minister to intervene. Green Party MP Ricardo Menendez March spoke to Corin Dann