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In the wake of the Hisco scandal, which saw ANZ chief executive David Hisco stood down last week over his personal expenses, Peters says the former prime minister should resign from the company where he is chairman of the board.
"That's a massive conflict of interest," he added.
"And then you've seen the capital requirements, which he's blamed on some low surrogate inside the bank. That again has been wrong."
Peters says he believes there is "much more to be unearthed".
"I think there's some serious questions that need to be answered," he added.
Regarding a potential resignation by Sir John, Peters said it was not up to him to decide. "It's the Governor of the Reserve Bank who could make that request. But if you were to ask me if I was the Governor of the Reserve Bank I would have asked for his resignation, yes."
"Because the capital requirements are designed so that we don't end up like for example Greece or Portugal where there are people lined up for kilometres down the street trying to get their money out because the banks didn't have enough by way of reserve," he added.