National has criticised Parliament's Speaker Trevor Mallard for pulling the pin on an inquiry into who leaked details of leader Simon Bridges' expenses to the media.

Bridges and Mallard have both expressed concern for the mental health of the leaker who sent a text message last week to both and to a media outlet asking them not to pursue the inquiry because of the impact it would have on their mental health.

National MP Gerry Brownlee, who is shadow leader of the House, questioned what had changed in the 24 hours between Mallard yesterday announcing the appointment of Michael Heron QC to lead the inquiry, and today's decision to discontinue it.

"The Speaker … was happy to appoint Mike Heron but today it's all off because he's decided that all the guilt lies with our caucus. That's a pretty unacceptable position for a Speaker to put themselves in," Brownlee told the Herald.

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"Clearly there is a duty to find that person. I think he's obfuscating his duty as a Speaker, quite frankly, if it turns out to be a staffer, [Mallard] is the head of the Parliamentary Service and he has a duty of care to every person who works in that place, and he's walking away from that."

National rejected Mallard's assertion that the leak could only have come from within the National Party.

"While that is possible, that is not his decision to make nor can he categorically make it based on the evidence," Brownlee said.

"The facts have not changed following publication of parts of the text message and the Speaker has no new information than when he announced the appointment of a QC to lead the inquiry yesterday."

National would continue to search for the person who leaked the information ahead of its publication to both ensure their wellbeing and to protect the integrity of the role of the Opposition, he said.

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Audrey Young: National leader Simon Bridges loses control of leak inquiry

Mallard today ruled it was a National Party matter and therefore not something Parliament needed to be involved in.

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"The existence of, and part of the detail of, a text both the Leader of the Opposition and I received last week has been reported on. It has now been confirmed to me that the person who leaked the details of the expenses and the texter are the same person.

"He or she has details of events that it is unlikely anyone outside the National Party would be privy to.

"The text is from someone who is clearly very disturbed and today's publicity will almost certainly make that worse. My priority is to get appropriate support to them whether they are an MP or a staff member."

Bridges told a media conference this morning he wanted the investigation continued.

Police had identified the person who sent the text message but would not reveal who it was.

"The text made clear to me that it was from the leaker ... [and that] the leaker was in the National caucus," Bridges said.

"It also made quite clear that this person had a long and serious mental health issue. It was my very clear view there would be significant harm to them if the investigation proceeded. It was a dark and concerning text message.

"I was very worried about it. I spoke to senior colleagues and then replied, saying my utmost concern was for the welfare of the person. Later that day I received expert advice on how to proceed. On Friday I informed the police with my clear concern being for the mental health and wellbeing of the individual.

"On Sunday evening police contacted me. They knew and had worked out the identity of the person concerned. They made clear the person was getting the help they needed."

Police confirmed they had spoken to the person.

"Police assessed the information supplied as a mental health issue requiring an immediate response," police said in a statement.

"Steps were taken as they are for any matter reported to police where there are immediate concerns for the welfare of an individual."

Police said they had dealt with the matter "entirely from a mental health perspective".

The texter had claimed to be inside the National Party and had leaked Bridges' expenses to punish him for being arrogant.

Bridges said it was important to get to the bottom of who leaked the material in order to protect the integrity of Parliament.

Speaking to the media in Auckland earlier today, Prime Minister Jacinda Ardern said the inquiry should be halted if it was proven the individual had mental health issues, and it was an internal matter for National.

"I would want to deal with that internally but that is a matter for the leader of the National Party.

"If indeed this is an issue that's come out of the caucus, and if there are indeed mental health issues, it would strike me it needs to be dealt with really sensitively. It is perhaps best dealt with internally than externally.

"Every party will deal with these things in their own way but I think ultimately, politicians - we are humans too - so we always need to make sure we have mechanisms in place to look after members of our team."

Deputy Prime Minister Winston Peters said Brownlee was talking "balderdash" and the National caucus remained the most likely cause of the leak.

"Calling for a massive inquiry at a great expense to the public is extravagant in the extreme," Peters said.

Where to get help

Mental Health Foundation: Free call or text 1737 any time for support from a trained counsellor.