Winston Peters says ANZ board chairman Sir John Key should resign, claiming he has a "massive conflict of interest".
Last week ANZ New Zealand chief executive David Hisco stood down over his personal use of corporate chauffeur cars and charging the company for wine storage.
His exit came after ANZ Bank was censured by the Reserve Bank in May for failing to have enough money on hand to cover risks or losses, and for failing to disclose that for more than four years.
ANZ New Zealand board chair, former prime minister Sir John Key, said the board was concerned about how Mr Hisco was "characterising certain expenses and transactions following an internal review of personal expenses".
Deputy Prime Minister and Foreign Minister Mr Peters has told TVNZ's Q+A in an interview for tonight's programme Sir John has a conflict of interest.
"I think it's wrong that Mr Key can he head of the ANZ in New Zealand and sit on the Australian equivalent as well. That's a massive conflict of interest," he said.
"And then you've seen the capital requirements, which he's blamed on some low surrogate inside the bank. That again has been wrong," he added.
"I think there's some serious questions that need to be answered, and there's much more to be unearthed in my view."
Asked should Sir John Key stand down, Mr Peters replied: "Well, that's not my role. 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."
Mr Peters said New Zealand should have a commission on inquiry into the operations of the Australian-owned banks in this country - something he says he called for countless times while in opposition.
In a statement, ANZ New Zealand said it will co-operate with requests from the Reserve Bank.
* Q+A is on TVNZ1 on Mondays at 9.30pm, and the episode is then available on TVNZ OnDemand and as a podcast in all the usual places.