A woman whose father died in the plane crash on Mt Erebus listened to Prime Minister Jacinda Ardern apologise to her and let out a sigh.

"It was like I had been holding my breath for 40 years and suddenly could breathe again."

Jacinta Penn is the daughter of first officer Gregory Cassin, who grew up in Napier. He died in the crash aged 37, along with all other passengers and crew aboard.

Penn described hearing the apology as "a surprisingly powerful moment".

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"Tears were shed," she said.

"It was so good to have a full and final statement that the pilots were not at fault and for the passengers and crew to have an apology for the actual accident."

Penn appreciated the apology coming from both the Government and Air New Zealand together.

"It was more meaningful. The whole event was planned with much care and that meant a lot too."

 Debris on Mt Erebus after the Air NZ plane crash in 1979. Photo / File
Debris on Mt Erebus after the Air NZ plane crash in 1979. Photo / File

The apology, which families had waited 40 years for, was made by Prime Minister Jacinda Ardern and Air New Zealand chairwoman Dame Therese Walsh at Government house in Auckland on Thursday.

"After 40 years, on behalf of today's Government, the time has come to apologise for the actions of an airline then in full state ownership; which ultimately caused the loss of the aircraft and the loss of those you loved," Ardern said.

The Prime Minister acknowledged how the actions and events following the tragedy had affected the families.

Debate raged afterwards as to whether the pilots or Air New Zealand were at fault. The Prime Minister stated unequivocally that the pilots were not at fault.

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"The pilots were not responsible for this tragedy and I stand here today to state that again.

"But those findings were not accepted by our Government then. That was wrong, it caused trauma on top of grief, and persecution on top of pain," Ardern said.

"It sent ripples and trauma across the country. But that loss and grief was compounded and undeniably worsened by the events that followed."

Dame Walsh apologised on behalf of the airline, acknowledging that 40 years ago they failed in their duty of care.

"I apologise again on behalf of the airline for the way in which the families of those lost on Mt Erebus were treated in the aftermath of the incident. Better care should have been taken of you," she said.