The Government says it will not appeal but has dodged questions around an apology after the High Court found MIQ infringed on the rights of New Zealanders.
National has welcomed the decision but says the Government needs to "apologise and move on".
The High Court in April said MIQ's combination of the virtual lobby and narrow emergency criteria meant New Zealanders' rights to enter the country were infringed.
Today Covid-19 Response Minister Ayesha Verrall confirmed the Government would not appeal the decision, based on legal advice that had come in "overnight".
"We know MIQ was a very important part of our process for keeping New Zealand safe. It averted tens of thousands of deaths.
"But we also know it put a major cost on people who sought to cross the border. And we want to acknowledge that that was very tough on people."
When asked if she or anyone else in the Government would apologise and if there would be any costs incurred, Verrall deflected and said they were still "digesting those aspects" of their legal advice.
Prime Minister Jacinda Ardern also did not address the question when asked if the Government would apologise, saying simply, "I'll leave it there".
National Party leader Christopher Luxon said it was "fantastic" the Government was not appealing but called for an apology.
"That's fantastic. That's the right decision. I just think it's just a very simple acknowledgement, either, whether it comes from Chris Hipkins or whether it comes from the Prime Minister.
"It's just acknowledging they got it wrong. And saying so. Apologise and move on."
Act Party leader David Seymour also called on the Government to apologise.
"The decision not to appeal the Grounded Kiwis case is an admission the Government got it wrong."
In the decision, Justice Jillian Mallon found that although MIQ was a critical component of the Government's elimination strategy, the combination of the virtual lobby and narrow emergency criteria meant New Zealanders' rights to enter their country were infringed.
"In some instances in a manner that was not demonstrably justified in a free and democratic society," Justice Mallon said.
Justice Mallon found that the MIQ system, focusing over the period from September 1 last year to December 17, didn't allow for individual circumstances to be considered and prioritised, and examples of extreme delays were not prioritised.
The MIQ booking system did not allow for the prioritisation of returning citizens due to the "virtual lobby" that operated as a lottery, and the criteria for emergency allocation was narrow and too tightly set.