Mrs Prime said some had argued that taking kukupa was allowed by tikanga, but a meeting at Motatau's Kaitoki Marae had imposed a rahui on the birds across the Ngati Hine rohe in 1996 because their numbers were so low. That rahui was still in place.
She could not speak for Ngai Tahu, from whose area the birds were thought to have come, but even if Maori had a customary right to eat kukupa, that had to be weighed up against kaitiakitanga and the responsibility to protect a threatened species.
Mrs Prime (Te Kapotai, Ngati Hine) said her call for Mr Tau's resignation was not related to Ngati Hine's opposition to Ngapuhi's current Treaty settlement process, but the kukupa incident did call into question his leadership ability.
Mr Tau has said he will not comment further while the incident is being investigated, but has undertaken to co-operate fully with any inquiry.
Meanwhile Mr Harris said he found it untenable to remain on Thoronuku in light of its leader's actions, Mr Tau's "mistake" making a mockery of the years he (Mr Harris) had spent educating Northland's young people about protected native birds.
"To have this happen is an absolute slap in the face," he said. "Sonny Tau needs to face the people. He needs to face Ngapuhi and man up to what he's done."
And it was important that kukupa continued to be protected.
"The population is not as high as it used to be. There is less forest. They face huge threats; there's humans, but they are also up against feral cats, pigs - there are a lot of dynamics," he said.
"It'd be quite selfish for the next generation to grow up without them."
David Rankin, a Ngapuhi descendant of Hone Heke, supported Mr Tau however.
"Sonny has done nothing wrong according to Ngapuhi tikanga, and Article 2 of the Treaty of Waitangi guarantees Maori the full, exclusive and undisturbed possession of our fauna and flora. Basically, the problem is that the law hasn't caught up with the Treaty," he said.
DOC has declined to comment while the investigation is under way.
Thoronuku deputy chairman Sam Napia said Mr Harris' resignation was "unfortunate."