Cyber-security advice that no hacking into the Treasury had occurred was not known to any minister when the Government made public statements last month that the Treasury had been hacked, Prime Minister Jacinda Ardern says.

Once the advice had been received, ministers had a discussion about the use of the word "hacking", but it was decided to leave the matter to the police investigation.

During her post-Cabinet press conference today, Ardern said that the head of the Government Communications Security Bureau, which has a special cyber-security unit, had disputed the language used to describe the access of Budget information two days before Budget day.

But Ardern said the GCSB phone call made to GCSB Minister Andrew Little did not happen until after statements from Finance Minister Grant Robertson and Treasury boss Gabriel Makhlouf had been released - which both referred to the incident as systematic hacking.

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"At the time the statements were made by Treasury and indeed the Minister of Finance, no minister received any advice at that point by the GCSB," Ardern said.

Robertson has previously said he did not know about the GCSB concerns when he put his statement out, but Little, who is overseas, has not endorsed Robertson's timeline, saying only that he had acted in a timely way and that he understood Robertson had acted appropriately.

Ardern has previously refused to comment, saying that the State Services Commission investigation into whether Makhlouf misled the Government should run its course.

But today she said that the GCSB phone call came "several hours" after Robertson's and Makhlouf's statements were released on Tuesday, May 28, two days before Budget day.

The following day, neither Ardern or Robertson revealed the GCSB advice despite being questioned repeatedly in the House about the so-called hack. and despite National leader Simon Bridges calling Robertson a "liar" for saying that the Treasury had been "hacked".

Ardern defended not doing so, saying ministers changed their language and a full picture of what had happened was yet to surface.

"Whilst there were different views on the language, there was no clarity around what in fact had happened ... that information was not received until Wednesday evening.

"This was a matter for the police, not a matter for us, and so that is where it was left."

Bridges dismissed this, repeating simply: "As I said before, they sat on a lie."

Police advice that nothing illegal had taken place was revealed on the morning of Budget day. National revealed a few hours later that staffers had access Budget information through the Treasury website's search bar.

National Party deputy leader Paula Bennett said it was "very convenient" that Ardern was happy to be "the mouthpiece for Andrew Little" now that he was not in the country.

She said Ardern was making matters worse by drip-feeding information after previously saying that she would not.

"She is yet again feeding a little bit of information that actually makes the whole picture even more cloudy and blurry. She has a responsibility as the Prime Minister of this country to come out and tell the whole truth so we understand who knew what, and when."

Bennett has called for the investigation into Makhlouf to be widened, and confirmed that investigation head John Ombler, the Deputy State Services Commissioner, will interview her and Bridges.

"If he is willing to interview the leader and deputy leader of the Opposition, then he has an obligation to interview the ministers involved," Bennett said.

Ardern said she expected the investigation to set out a timeline of events, including the GCSB call to Little, even though the commission has no jurisdiction over ministers and terms of reference are about Makhlouf, his advice to Robertson, and why he called in the police.