Mr Tipene said the group thought Mr Tau needed to do more than step down from his position as chairman of Tuhoronuku, including standing down as chairman of the Ngapuhi Runanga.
"If he steps down from one position he should step down from other key positions. It's untenable that a leader who admitted guilt should hold these positions."
Te Tai Tokerau MP Kelvin Davis said Mr Tau had made the "right move" but said he also needed to consider his role in other positions.
"It would be untenable for him to remain as chair of the runanga and I think he should step down from other positions such as whanau ora and the Iwi Leaders Forum."
Mr Davis said Mr Tau needed to "test the support" he had by resigning and seeking the positions again.
"It's quite serious. He should step down and test his mandate again. If people are confident in his abilities then they will vote him back, it's a chance for him to prove his support."
Mita Harris, a former Tuhoronuku representative and Northland Conservation Board chairman, said Mr Tau stepping down "was the right thing to do" but more needed to be done.
"There needs to be tikanga. There needs to be an apology to hapu in the South Island and he also needs to broadcast an apology to all people of Ngapuhi - it's not over."
Mr Harris, a relative of Mr Tau, announced last week he had stepped down as the Ngati Toro hapu representative on Tuhoronuku over the kukupa scandal. He said he knew there had been pressure placed on Mr Tau with his two positions.
"He needs to reconsider his future as leader at the moment, the board members need to look at his whole leadership. He was only interim chair of Tuhoronuku - he holds two positions and he needs to consider his other position."
Mr Tipene said he did not think Mr Tau's decision to step down would impact the current treaty negotiations.
Mr Harris said he would not be rejoining Tuhoronuku at this stage.
"I'm watching with interest," he said.
Mr Tau will remain on Tuhoronuku's 22-strong board.
Deputy chairman Sam Napia was appointed acting chairman and Moana Tuwhare was elected deputy chairwoman.