DoC Operations Manager Stephen Stoole said the attempts to re-float the surviving mature whale had been unsuccessful.
''The whale's condition is deteriorating, she is in distress and unlikely to survive,'' he said.
"Those with the whales did all they could to keep them comfortable and attempt refloating. A big thanks to Te Roroa, Te Uri o Hau, Project Jonah, Ingrid Visser and her team and Northland locals who worked alongside DoC staff to help the whales as much as possible.
''This is a sad outcome and a decision not taken lightly."
A DoC employee with the relevant expertise is travelling to the ocean beach west of Dargaville to humanely end the misery of the weak whale this morning.
Police and other emergency services were called in at about 8.30am this morning to clear the beach.
Snow Tane, chief executive of Te Roroa Trust, and trust chairman Sonny Nesbit said the news was extremely sad.
They had been on the beach with others from his iwi and neighbouring Te Uri o Hau hapu since the whales came ashore.
The stranding is right on the boundary of Te Roroa and neighbouring iwi to the south, Te Uri o Hau. Both will be involved with the flensing - the breaking down of the carcass of the smaller whale which died yesterday.
It is not yet decided what will happen to the larger one one after it dies.
The refloating attempt yesterday failed after a huge trench was dug which, when filled with the incoming hight tide, rescuers hoped would provide a channel for the whale to reach the sea.
Although seawater rushed in and surrounded it, there was not enough to get the huge bulk off the sand.
While the whale responded to the feel of water by slapping its tail for the first time in hours, it appeared very weak.
The ''soft'' tide at 5pm yesterday afternoon and again around 6am today were not high enough to help the whale back to the sea.
Before the hard call was made to end the creature's suffering, over a 48-hour period a trained army of experts and volunteers struggled to keep the animal moist and cool on the open ocean beach and a changing crowd of community members stood in vigil behind a roped-off area.
The euthanasia was expected to take place at midday.
The whales were marooned two kilometres south of the Baylys Beach settlement on the 100km Ripiro Beach west of Dargaville.
Over the past two days hundreds of people have been on the beach, including trained whale rescue volunteers, emergency services and members of the public who were part of the human chain passing buckets of seawater to keep the animal wet.
