She added that she had never eaten the protected bird. "I don't like game. My stomach has become very Anglicised."
However, she supported Ngati Rangi's decision to offer it at what they considered a special occasion.
"They chose to offer that because it is one of the most significant delicacies we have. I think based on what they believe I probably would support them."
Dame Tariana said a cultural take should be allowed but only for special occasions for a marae. The bird was depleted not because Maori were eating them, but because deforestation, exotic species and water pollution had destroyed much of their habitat, she said.
"To me, the issue is that our people are being criminalised for what was a normal practice."
However, Ms Barry rejected that, and said there were health and safety issues with eating birds that had been frozen for a long time and with no information about how they died.
DoC was explicit in its documentation when handing over birds that they were not for consumption.
"These birds could have been road kill, could have been poisoned, could have been shot.
The very idea that you would offer them for human consumption beggars belief...when was the last time you ate roadkill, I mean why would you?"
In the past DoC had removed the feathers and bones itself before handing them over and disposing of the rest of the bird.
Asked if that practice could resume instead of handing over whole kereru, Ms Barry said weavers liked to pluck or supervise the plucking of birds so feathers could be more readily woven into cloaks.
Prime Minister John Key said the other two ministers at Maungarongo marae - Amy Adams and Nathan Guy - were completely unaware kereru was served.
"But if the marae is saying they served it, they would certainly know ... but when you go to a marae, usually it is communal and people are dining with lots of different dishes put in the middle, some of which people eat, and some of which people don't."
Marae spokesman Che Wilson told the Herald between three and five birds were given to them by the Department of Conservation over an 18-month period.
Feathers were used for weaving and the birds saved for special occasions such as the leaders' hui. He said DoC was unaware that the birds would be eaten.
"They were dead birds DoC had and gave to us. They didn't have enough room in their freezer, so they gave them to us over about 18 months."
The kereru were served with miro berries.
The latest controversy comes as Northland leader Sonny Tau is being prosecuted under the Wildlife Act after he was found with kereru at Invercargill airport.