The whales became stranded on Puponga Beach near Farewell Spit in the north of the South Island on Tuesday as the tide went out, said John Mason, a local conservation department official.
The whales were being kept damp with buckets of water and wet sheets by about 100 volunteers, Mason said, but the volunteers were to be withdrawn when darkness fell.
"It's really too dangerous to have people in the sea with the whales," Mason said.
Three whales had died by Tuesday evening but it was hoped some would refloat themselves at high tide on Wednesday morning.
There would be a second chance to save some of the animals at the following high tide on Wednesday afternoon.
"We'll be able to try and refloat them with human assistance," Mason said.
The whales were first seen off the beach in the morning, milling around near the shore.
"It wasn't a great surprise to us when they began to strand when the tide turned and began to go out."
The first whale was stranded about 2:00pm (0100 GMT) and the rest of the pod of whales, measuring four to five metres in length (13 to 16 feet), had progressively become stuck on the sand.