Newly appointed Auditor-General Martin Matthews' immediate future in the role is being questioned after his handling of an investigation of a major fraud carried out under his nose was referred for an independent inquiry.

Mr Matthews was head of the Ministry of Transport when fraudster Joanne Harrison stole $726,000 in a series of scams for which she was jailed for three and a half years in February this year.

State Services Commissioner Peter Hughes is considering a new investigation into the way the ministry handled the case after receiving a request to do so.

There have been calls for Mr Matthews, who left the ministry in June last year and was appointed to his new role by a government panel in November, should step down while an investigation is carried out.

The latest allegations include that two minister staffers were made redundant within weeks of raising concerns about Ms Harrison's behaviour, and that Mr Matthews didn't properly act on concerns raised by other staff.

NZ First leader Winston Peters said the selection panel that appointed Mr Matthews was not fully informed when they made their decision.

"They had nowhere near the facts that they needed and that's a serious issue as well," he said.

"I'm worried about getting all the facts out as fast as I can and ensuring that he stands down."

Labour leader Andrew Little has maintained he has confidence in the Office of the Auditor-General but said it was a matter of public confidence to have issues around Mr Matthews resolved.

"I think the right thing for the Speaker to do would be to reconvene the (appointment) panel with all of the available information, including information that comes out of the State Services Commission inquiry, to decide on whether or not any of that new information is sufficient to change their minds about the original recommendation," he said earlier on Tuesday.

Mr Little said he was aware of Mr Matthews' role in investigating Ms Harrison and had supported his appointment based on a briefing from the Serious Fraud Office including that it was Mr Matthews' actions that allowed Ms Harrison to be prosected.

Prime Minister Bill English said it would be a concern if public service employees were being unfairly treated and if there was new information the State Services Commissioner or new Ministry of Transport chief executive Peter Mersi should look into it.

But he said it was "quite inappropriate" for the government to comment on the Auditor-General, including whether he should continue in the role during an investigation, given his role as an independent government scrutineer.