"What's happened is a tragic mistake. But we're angry these birds have been shot after the shooters were instructed to shoot pukeko on the wing, having been told that takahe can't fly."
Mr Braddock said DoC needed to investigate to find out how that happened, and what action had been taken.
Despite the tragedy, Mr Braddock defended the pukeko cull as necessary.
He said pukeko posed a real threat to the eggs and chicks of takahe, pateke, shore plover and the other native birds released on Motutapu.
"They're also a real problem with our planting programme to expand the native forest on Motutapu. The pukeko rip the native tree seedlings from the ground virtually the day after our volunteers have planted them."
The takahe deaths were a setback, he said.
"But takahe have had many setbacks since they were rediscovered in Fiordland in 1948. We'll get over this and move forward.
"There are 300 takahe in the world and we've just had a very successful breeding season adding 40 takahe chicks to the population.
"The recovery programme is in good shape and we will all continue our work to secure the survival of these special birds for future generations."
Bill O'Leary, president of the Deerstalkers' Association, said he was embarrassed and upset to hear about the takahe being shot.
"I do know that the people involved in the group are very, very upset themselves.
"It's very difficult to deal with," he said.
South Island iwi Ngai Tahu are understood to be angry about the deaths, and Mr O'Leary said he had been considering how best to approach the iwi to offer an apology.
"We haven't had a chance at this stage, we've certainly been thinking about how we approach that."
DoC's northern conservation services director Andrew Baucke said the pukeko cull was undertaken by "experienced members" of the local deerstalkers association.
DoC was in talks with the association, which was said to be "co-operating fully" with inquiries.
Mr Baucke said takahe and pukeko had similar colouring and could be mistaken for each other.
The hunters were carefully briefed on how to tell the difference between them, including instructions to only shoot birds on the wing, he said.
"Guidelines introduced after an incident on Mana Island seven years ago when another takahe was mistakenly shot during a pukeko cull were also used during last week's cull."
Mr Baucke said the deaths were "deeply disappointing" for DoC and the volunteers. All culling operations had been put on hold while a review took place.
The takahe on Motutapu had been translocated from the Fiordland National Park, where the only wild population of the birds is based.
Pukeko are as common as ducks and geese and because they are a highly aggressive species they are considered a threat to rare native bird species.
Takahe were thought to be extinct in the early 20th century but were rediscovered in 1948 in the South Island. Two-thirds of the population are now based in "safe sites" including Motutapu, while around 100 live in the wild within Fiordland National Park.