New Zealand First Minister Shane Jones says Māori MPs are taking strong exception to National MP Chris Bishop drawing references to the whānau links between Deputy Police Commissioner Wally Haumaha and New Zealand First deputy Fletcher Tabuteau.

Jones said National had essentially labelled Tabuteau and leader Winston Peters as "somehow not passing the test of parliamentary probity" and called on Speaker Trevor Mallard to do something about it.

"I'm not suggesting that Mr Bishop is anti-Māori and quite frankly I don't care if he is," said Jones.

"But it is an important principle with the number of Māori in the House whether they are urban Māori or broader traditional Māori, that you contemplate that situation because we are not going to put up with it for one day more."

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Haumaha's appointment process is set to be reviewed by Mary Scholtens QC to determine whether the State Services Commission panel sought or passed on to the cabinet all the relevant information required when making the recommendation.

The review was ordered in the light of revelations of supportive comments he made about former friends who were accused in 2004 of the rape of Louise Nicholas, for which he has apologised.

But National has also said that Haumaha's close links to New Zealand First MPs should have been declared to the cabinet before it decided.

National deputy leader Paula Bennett took exception to Shane Jones' objections in the House: "As one of those Māori there is actually also a convention that we express our conflicts of interest for whānau and particularly when we are looking at making statutory appointment and this side of the House has a right to question that."

Peters spoke at a marae celebration for Haumaha's promotion last year to Assistant Commissioner but insists that the police asked him. Tabuteau mentioned Haumaha as whānau in his maiden statement.

Tabuteau is a member of the executive as an under-secretary although not a member of the cabinet which signed off on the Deputy's appointment in May.

Bishop told the Herald later there was an implication was that he was being racist by raising the family connection.

"There are links between various members of New Zealand First and Mr Haumaha," Bishop said.

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"It is an extremely important office that he has been appointed to and we are doing our job as responsible members of the Opposition in investigating whether or not the appointment of Mr Haumaha has integrity."

Jones' objections came after Bishop asked Prime Minister Jacinda Ardern if she had confidence in the professional independence from Mr Haumaha "when her Police Minister gives him a shout-out in his workout videos, her Deputy Prime Minister [Peters] attended a celebration on a marae for his appointment as Assistant Commissioner, her Foreign Affairs under-secretary has whanau links to him and he was previously announced as a candidate for New Zealand First?"

Peters said outside the House that Bishop was talking about "a tissue of lies."