The Labour Party says a wider review of the Accident Compensation Corporation is necessary to fix long-standing problems and reassure the public.
The Privacy Commissioner is investigating privacy breaches at ACC, while the Auditor-General is looking at how the corporation manages risk.
Labour's ACC spokesperson Andrew Little said on Monday that ACC Minister Judith Collins must consider a broader inquiry.
"The level of public confidence is low - particularly amongst many claimants - and something needs to be done to restore that public confidence.
"It's in the hands of the minister to do something and I think commissioning a broader inquiry at a professional sort of level is the sort of action that's needed."
However, Prime Minister John Key said on Monday it is best to wait for the results of the current inquires first.
"There's some genuine questions that would need to be answered about the rationale for the statements that were made by the executives at ACC - but that's a matter for them ultimately and indeed, in the fullness of time, the minister to get a better understanding of.
"But I think the minister would prefer to wait and see all of the investigations currently on the go completed."
Greens want ACC board chair stood down
On Monday, the Green Party called for ACC board chairman John Judge to be stood down.
Claimant Bronwyn Pullar, who is at the centre of a dispute with the corporation, has spoken publicly in a television interview.
Green MP Kevin Hague said the interview which screened on Sunday highlighted problems with ACC claims management, shonky assessments and deliberate attempts to target people on long-term compensation.
He said it is clear that ACC Minister Judith Collins needs to act urgently and remove Mr Judge from his role.
Mr Hague says that role is about both the minister's and the public's trust and confidence in ACC, which must be under extreme stress.
Judith Collins says a high priority for ACC is to promote and rebuild the trust and confidence the public can rightly expect to have in the corporation.
