Prime Minister Jacinda Ardern will not be drawn on whether Treasury Secretary Gabriel Makhlouf should be sacked, but has suggested that the State Services Commission may look into whether he misled the Government.

Last week the commission launched an inquiry into how confidential Budget material was accessed at the Treasury, but it had yet to decide whether to investigate Makhlouf's behaviour.

National leader Simon Bridges has called for both Makhlouf and Finance Minister Grant Robertson to resign for what he said was knowingly smearing the National Party by implying that National had hacked the Treasury website.

Party staffers had simply found Budget 2019 information by using the website's search function.

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After National started to release Budget 2019 information ahead of Budget day, Makhlouf said last Tuesday that the Treasury had been "deliberately and systematically hacked".

He called the Police, citing advice from the National Cyber Security Centre (NCSC), an arm of the Government Communications Security Bureau (GCSB).

That reference escalated the seriousness of the issue and how the information was accessed, which was reinforced the following morning when Makhlouf said publicly that there had been 2000 attempts to access information in 48 hours.

However the NCSC said in a statement that the Treasury's computer system was not compromised.

"Given the incident did not involve a compromise of the Treasury computer network and was therefore not the type of incident the NCSC would normally respond to it was recommended that the matter be referred to police for their assessment."

Police told the Treasury the following day that nothing unlawful appeared to have happened, but this was not revealed until the Treasury released a statement on Friday morning at 5am.

Bridges then called for Makhlouf to resign, adding that Robertson should resign as well because he was "donkey deep" in this.

National deputy leader Paula Bennett has also written to the commission, asking it to investigate whether Makhlouf and Robertson had misled New Zealanders.

Asked about the Bennett's letter, Ardern said she would wait and see the outcome of the commission's inquiry.

"I imagine that will answer some of the questions there," she told Newstalk ZB.

"Ultimately the Minister of Finance, or any minister, does rely on the advice that they're provided by their departments. They have to be able to know that will be reliable advice, and that's what the State Services Commission is looking at."

On Tuesday night, after Makhlouf's statement, Robertson said: "We have contacted the National Party tonight to request that they do not release any further material, given that the Treasury said they have sufficient evidence that indicates the material is a result of a systematic hack and is now subject to a Police investigation."

In the following days, Ardern and Robertson said that no one was implying that National had hacked the Treasury website.

The commission cannot investigate whether Robertson's comments have been appropriate, as its jurisdiction does not include ministers.

Bridges also called for Deputy Prime Minister Winston Peters to publicly apologise for saying National had acted illegally - but Peters has stood by his comments.

"Treasury has known since Tuesday exactly what happened and they covered it up to hide their incompetence," Bridges has said.

"They have sat on a lie, calling the National Party criminal hackers and calling in the police."

On Friday a spokesman for the commission said that State Services Commissioner Peter Hughes was considering the allegations made by Bridges around whether Makhlouf smeared National, or misled the Minister of Finance.