The group's scientific advisor Jaycee Tipene-Thomas said the bones would be buried at an undisclosed location while the other remains at another location.
She said the bones would be dug up in an year or two and would be kept as taonga.
Earlier today, DoC spokeswoman Abi Monteith said it would be logistically challenging to move the whales.
She said the digger could not do it because the mammals were too heavy and the machine did not have the right parts to carry out the work.
DoC believes the whales are so rare they have only been sighted at sea 30 times.
They are mostly found in Antarctic waters- Taupō Bay was near the northern limit of their range- and they were a pelagic, or migratory, species.