Christchurch City councillor and insurance advocate Ali Jones wants the State Services Commissioner to broaden his inquiry into the Earthquake Commission beyond problems with its customer satisfaction survey.
The minister responsible for EQC, Gerry Brownlee, has asked for an inquiry into the survey which appears to leave out customers who have complained.
On Wednesday the EQC admitted that about 31,000 claims have been unintentionally excluded from customer surveys in the past three years.
Mr Brownlee says he's extremely unhappy about what has happened and refused to comment when asked if the job of the EQC chief executive Ian Simpson was safe.
Ms Jones says the problems at EQC run deeper than a botched customer satisfaction survey and that senior managers within the organisation are refusing to engage with anybody who criticises them.
She says that it may be time for Ian Simpson to resign but that other managers should also take responsibility.
Mr Simpson has yet to respond to a request to be interviewed by Radio New Zealand.
The Labour Party says that as the minister responsible for the Earthquake Commission, Mr Brownlee, is to blame for the agency's failings.
Labour's Earthquake Recovery spokesperson, Clayton Cosgrove, says he wouldn't be surprised if Mr Brownlee sacked Ian Simpson and used him as a scapegoat for his own failure to keep a closer rein on the EQC.
Mr Cosgrove says there have been enough inquiries into the EQC and the minister now needs to take action.