An investigation into whether Treasury boss Gabriel Makhlouf misled the Government will not probe into whether senior ministers acted appropriately.
But the National Party says it is critical to the Government's integrity for the actions of Prime Minister Jacinda Ardern, Finance Minister Grant Robertson and Government Communications Security Bureau Minister Andrew Little to be scrutinised.
Depending on the outcome of the State Services Commission investigation, National will consider asking for a public inquiry to be ordered, and it is going to use Question Time to try to extract answers.
At issue is the urgent phone call from the GCSB to Little last Tuesday, May 28, to relay its strong objections to the access of confidential Budget information being characterised as a systematic hack.
Government ministers spent the following day, May 29, staying mum on the GCSB phone call and quietly changing the language by describing it as an "attack" on the Treasury.
National has accused the Treasury and Robertson of smearing the National Party by implying that it had hacked the Treasury website when they knew that no hacking had taken place.
Robertson has said that he was not informed about the GCSB's objections before he released a public statement on Tuesday, May 28, that called it systematic hacking.
Yesterday Little refused to endorse Robertson's recollection, saying only "from what I know and understand, [Robertson] has acted with absolute propriety".
Little also would not comment about why the Government, after being told about the GCSB objections, did not clarify what had happened for over 24 hours.
"I'm reluctant to get into detail because there is an investigation under way," Little said.
"If it looks like ministers are starting to chip in with their version of various stories, when any of us only ever has one part of the story, it has the potential to undermine the State Services Commission investigation."
Little said neither he or his office had been contacted by the investigation.
"I'm very relaxed about any information I received and the way I handled it ... I'm available for any investigation."
National deputy leader Paula Bennett said that response was "rubbish" because ministers knew that they were outside the jurisdiction of the State Services Commission.
"They're hiding behind an inquiry they cannot partake in, and aren't being wholesome with the truth."
While the investigation can interview ministers in relation to its questions about Makhlouf, the commission cannot criticise or investigate ministers as that is outside its legal scope.
State Services Commissioner Peter Hughes told the Herald that the investigation's focus had not changed.
"As previously stated, the focus of the investigation is to establish the facts in relation to Mr Makhlouf's public statements about the causes of the unauthorised access; the advice he provided to his Minister at the time; his basis for making those statements and providing that advice; and the decision to refer the matter to the Police.
"[Deputy State Services Commissioner John] Ombler (who is leading the investigation) will talk to the individuals he needs to in order to establish the facts," Hughes said.
Bennett said it was crucial for the investigation to look into ministers' behaviour, and if it did not, National would consider asking for a government or public inquiry - though these would have to be initiated by a minister or by Order in Council.
"It's now integral for the integrity of this Cabinet that they come forward and say what they knew, when, and tell the whole truth," Bennett said.
National would also pursue answers in Question Time and through the Official Information Act.
Little said he was confident the Government had done everything it should have with the information it had.