Prime Minister Jacinda Ardern has not ruled out re-opening the position of Deputy Police Commissioner for appointment, depending on the result of the inquiry into the process.

She has said that in the event of the inquiry showing deficiencies in the process, she would consult the Solicitor General or State Services Commissioner on next steps.

Asked today if that meant the appointment could be re-opened she said "that of course would be pending."

Mary Scholtens QC is set to conduct a Government inquiry into whether the appointment panel had all the relevant information before making the appointment.

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"If then questions are raised over whether we had all the information we needed and the finding is that we didn't, then it would be appropriate for the appointment itself to be looked at - but not by us," Ardern told reporters at Parliament this morning.

Wally Haumaha was appointed Deputy Commissioner in May in a statutory appointment that is singed off by the Governor-General on the recommendation of the Prime Minister.

In reality, applicants were assessed by a panel comprising State Services Commissioner Peter Hughes, Deputy Debbie Power and Police Commissioner Mike Bush, and they sent a short-list of two to Police Minister Stuart Nash.

At the heart of the issue is whether the panel and ministers knew or should have known about Haumaha's support for his former colleagues in 2004 who were accused of the rape of Louise Nicholas.

Nash reiterated today that Bush had told him that he did not know about comments made during the course of Operation Austin.

But Haumaha's promotion last year as Assistant Commissioner was controversial for the same reason – and that suggests that Bush should have anticipated problems with further promotion.

Other issues have emerged including more recent allegations by staff at Justice and Corrections that Haumaha had acted in a bullying way when they were jointly working on a project at Police National Headquarters.

Today's revelation that Haumaha last week contacted a witness to the alleged bullying in a bid to shore up support after the Herald started making inquiries have sparked suggestions that Haumaha stand aside while the inquiry is being conducted.

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But that is not flying, even within the Government where levels of frustration are high.

Nash dismissed the notion.

"There is a process of natural justice and we have got to let it follow its course," he told reporters.

"We have set up a process and I want to see the process followed through.

"At the end of that, let's see what comes out and let's see what decision we make but at this point I am not going to ask Wally Haumaha to stand aside."

He said the police were looking at the claims over Haumaha contacting a witness.

"The Police are not trying to cover this up in any way, shape or form."

When the inquiry was first established, under Acting Prime Minister Winston Peters, there was no suggestion that the job could be re-opened. All the emphasis was on looking only at the process.

The first inquirer, Pauline Kingi, resigned after revelations she had extensively endorsed Haumaha on social media. Scholtens was appointed last week and a reference to next steps including the Solicitor General and State Services Commissioner were made for the first time.

National's police spokesman, Chris Bishop, questioned whether Haumaha's position was tenable.

"You have to say, as every day goes by and more and more alarming allegations and revelations are revealed you have to wonder if his position is tenable."

But he said it was a matter for the Prime Minister and the cabinet.

"At the end of the day the appointment of Wally Haumaha is their appointment, they need to be accountable for why he was appointed and for the conduct of the inquiry and the process of the inquiry into that appointment."