There is now a cloud over the Office of the Auditor-General and it is untenable for Martin Matthews to remain in his role, the Green Party says.
Mr Matthews stood down as Auditor-General in May when an inquiry was launched into his suitability after it was revealed a fraud took place while he was in charge at the Transport Ministry.
Senior manager Joanne Harrison stole nearly $750,000 over several years, despite staff repeatedly raising concerns about her with Mr Matthews.
The Officers of Parliament committee received the inquiry report several weeks ago and then met repeatedly to discuss the matter - but the report has not been made public or any decision announced.
Green Party co-leader James Shaw said the integrity of the Office of the Auditor-General should be paramount.
"There is now a cloud over the office and so I actually don't think that it is tenable for him to continue in that [job] given that.
''It is a murky situation but it is absolutely important that the integrity of that office is maintained.
''I think it is very difficult for him to continue in that role," he said.
Prime Minister Bill English said everyone benefited if the matter was promptly resolved.
"It's better for everybody if it resolved sooner, but the ... [committee] will have to follow due process," Mr English said.