Police investigating claim Deputy Police Commissioner Wally Haumaha phoned witness to bullying incident

Police Minister Stuart Nash says he is "frustrated" and "annoyed" as allegations against Deputy Police Commissioner Wally Haumaha continue to surface ahead of a Government inquiry into his appointment.

A police investigation is underway into allegations the Deputy Police Commissioner called a key witness in a bullying incident and tried to rally their support.

It's claimed that Wally Haumaha phoned a lower ranking officer who had intervened in an exchange between himself and three female staff in 2016.

According to NZME, the call happened last week after it began asking questions about the incident. The officer who was called reported the incident.

NZME reported that three women left Police National Headquarters and worked from a new location because of Mr Haumaha's alleged behaviour.

Prime Minister Jacinda Ardern said she's also frustrated by the continued reports that are emerging about Mr Haumaha.

"Anyone who's employed anyone before would know the frustration of not having the information we needed to make the decision in a timely way, in an appropriate way. I am frustrated.

"I want this to move quickly but I also want to get it right, that's why we have an independent person assisting us with that."

Police Minister Stuart Nash said: "I'd be lying if I didn't say I wasn't frustrated by what's happening at the moment and a little bit annoyed to be honest."

He said he had confidence in police to fully investigate the allegations about the phone call and the alleged bullying.

Mr Nash said neither he nor the Government would ask Mr Haumaha to step down, "because I fully believe there is a process we need to go through".

He said whether to stand Mr Haumaha down would be a decision for police, and under the constitution he could not tell police what to do.

"I do believe in natural justice. I know there is a process underway, and keeping in mind we do live in a democracy I can't go firing people willy nilly."

Mr Nash said the inquiry is "about the process not the person" and whether he was given the appropriate information before he recommended Mr Haumaha to Prime Minister Jacinda Ardern for the role. 

Police Commissioner Mike Bush said in a statement to Newshub: "The Police Executive were made aware on Friday of contact between Deputy Commissioner Haumaha and a staff member in relation to bullying allegations. This will be investigated and we are currently seeking further information about what has occurred to determine what steps are required."

Commissioner Bush said police have received no complaints in relation to the bullying allegations, but will reach out to the agencies and people concerned to give them the opportunity to talk.

"The Police Executive, including DC Haumaha, recognise the need to ensure that there is an appropriate level of independence to any investigation of all the matters raised in the media recently, including this most recent allegation," he said.

An inquiry into Mr Haumaha's appointment as Deputy Police Commissioner will commence on August 20, led by Mary Scholtens QC.

Its purpose is to examine, identify and report on the adequacy of the process that led to Mr Haumaha being appointed.