Prime Minister Jacinda Ardern says there are no conflicts of interest between New Zealand First Ministers or MPs and the inquiry into the process used to appoint Deputy Police Commissioner Wally Haumaha.
The investigation will look at the process that led to Mr Haumaha being made deputy police commissioner - despite comments he made defending police officers accused of rape in 2004.
The New Zealand Herald reported that NZ First's deputy leader Fletcher Tabuteau is from the same iwi as Mr Haumaha and that Winston Peters spoke at a function on the marae to celebrate Mr Haumaha's promotion.
National's Chris Bishop said that was a clear conflict of interest.
"Wally Haumaha was certainly reported to be a New Zealand First candidate in 2005. The family member of a New Zealand First Under-Secretary Fletcher Tabuteau. He and one of Winston Peters' close associates Tommy Gear are on the same marae. Winston Peters actually attended a celebration on that same marae alongside Mr Wally Haumaha," he said.
He said NZ First Minister Tracey Martin, who was appointing someone to lead the inquiry, should step aside.
"What the Cabinet should do and what Prime Minister Ardern should do is set Tracey Martin aside and have a genuinely independent inquiry that has no New Zealand First involvement whatsoever."
"This is a very serious and significant matter ... It's absolutely vital that the inquiry into Mr Haumaha's appointment be absolutely full of integrity and at the moment I don't think you could say that."
However, Ms Ardern remained adamant there was no conflict of interest.
"No individual party is dealing with that issue, the government is dealing with the issue in Cabinet.
It was completely suitable that Ms Martin would be involved as the minister in charge of the appropriate department for independent inquiries, Ms Ardern said.
"We are taking these decisions as a Cabinet, I have no concerns around any conflict of interest," she said.
"Just to be clear, the Minister for Internal Affairs basically sits over the process of an inquiry rather than the inquiry and the outcomes itself. They bring in the recommendations on who might undertake the inquiry that's on recommendation."
"Ultimately though, all of this comes back to Cabinet and our decisions are taken by the government as a whole."
An announcement on who will lead the inquiry was expected this week, Ms Ardern said.