The Air New Zealand plane from Brisbane on Australia's east coast was approaching Auckland Airport when the woman went into labour, local media reported on Saturday.

Two nurses who were passengers on the flight assisted the woman during the delivery - but were not able to save the life of the newborn baby, the Middlemore Hospital spokeswoman said.

Paramedics met the plane and took the woman and baby to the hospital. The passenger was in stable condition and the baby appeared to have been stillborn, said the hospital spokeswoman, speaking on usual condition of anonymity.

"We have no reason to believe Air New Zealand did anything remiss. They did everything they could,'' she told the Dominion Post newspaper.

The baby was believed to have been about five-six weeks premature and the mother was 34 weeks pregnant, within Air New Zealand guidelines for flying when pregnant.