About 300 have already died at Farewell Spit, on the South Island, in one of the worst such cases in the country.
Hundreds of locals and conservation department staff have been trying to save the survivors since early Friday morning, and have formed a human chain to refloat the whales.
Scientists do not know what exactly causes whales to beach themselves.
But it sometimes happens because the whales are old and sick, injured, or make navigational errors particularly along gentle sloping beaches.
Sometimes when one whale is beached, it will send out a distress signal attracting other members of its pod, who then also get stranded by a receding tide.
The conservation department said it had received a report about a possible stranding on Thursday night, but did not launch the rescue operation until Friday morning as it was too dangerous to attempt a rescue in the dark, reported the New Zealand Herald.
Andrew Lamason, the departments regional manager, said it was one of the largest mass beachings recorded in New Zealand.
New Zealand marine mammal charity Project Jonah. which is leading efforts to save the whales said a total of 416 whales were stranded.
It said the surviving whales are "being kept cool, calm and comfortable" by medics and members of the public.
Some of the refloated whales tried to swim back to shore, and the human chain was trying to herd them out to deeper waters, said volunteer Ana Wiles.
She told news outlet Stuff that there were "so many fins in the air, no breathing".
"We managed to float quite a few whales off and there were an awful lot of dead ones in the shallows so it was really, really sad."
"One of the nicest things was we managed to float off a couple [of whales] and they had babies and the babies were following," Ms Wiles added.
New Zealand has one of the highest stranding rates in the world, with about 300 dolphins and whales ending up on beaches every year, according to Project Jonah..
Many of these incidents happen at Farewell Spit. Experts say its shallow waters seems to confuse whales and hinder their ability to navigate.
In February 2015 about 200 whales beached themselves at the same location, of which at least half died.

It was due to be held at Queen's University in Belfast in June.
In an email to delegates, the university's vice chancellor Patrick Johnston said he had made the decision on Monday that the event would not proceed.
He cited concerns about the security risk for delegates and about the reputation of the university.
The symposium: Understanding Charlie: New perspectives on contemporary citizenship after Charlie Hebdo, was due to be hosted by QUB's Institute for Collaborative Research in the Humanities.
Twelve people died when two brothers, Said and Cherif Kouachi, fired on the journalists on 7 January at the satirical magazine's offices in Paris.
Five others were killed over the two following days by one of their associates.
Volunteers in New Zealand are racing to rescue survivors after more than 400 pilot whales beached themselves.
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A conference in Belfast to discuss the fallout from the Charlie Hebdo murders has been cancelled.