Prime Minister John Key continues to have confidence in Education Minister Hekia Parata despite renewed calls for her to be sacked.
Opposition parties say Ms Parata needs to be held to account for failures in education and should follow Secretary of Education Lesley Longstone in resigning.
Mrs Longstone's resignation follows a series of problems at the ministry including failures with the Novopay payroll system, Christchurch school reforms and the High Court's overturning of a decision to close a special needs girls' school in Nelson.
Announcing the resignation on Wednesday, State Services Commissioner Iain Rennie said the relationship with Ms Parata was a factor.
In a statement, Mr Key said he has complete confidence in Ms Parata as a minister.
Labour's deputy leader Grant Robertson said the Secretary for Education appears to be taking the fall for the litany of problems at the ministry.
Mr Robertson said Ms Parata is driving the policy and should resign, and if she won't accept responsibility on her own, the Prime Minister has to step in.
The Green Party says the Prime Minister cannot continue to back a minister who has lost the confidence of the entire education sector.
New Zealand First says Hekia Parata inherited policies that were doomed to fail and John Key is hanging his minister out to dry.
Education leaders say the ministry could have handled the series of problems better but Mrs Longstone never stood a chance.
They say the Government's policies were always going to be unpopular and Mrs Longstone, who came from England a year ago to take up the job, did not have time to get to grips with the intricacies of the New Zealand education system.
Principals Federation president Paul Drummond says Mrs Longstone was restructuring the ministry at the same time as being required to implement reforms, and was probably destined to fail.
"There were perhaps errors made or poor advice, and ultimately that's led to perhaps where we are today."
New Zealand Educational Institute secretary Paul Goulter said Mrs Longstone became the fall guy for a set of failed education policies.
The Public Service Assocation represents many workers in the Ministry of Education and its secretary, Brenda Pilott, says poor decision-making in the education sector is the joint responsibility of Mrs Longstone and Ms Parata.
Ms Pilott told Radio New Zealand's Morning Report programme there are some who feel the weight of blame falls mainly with the minister but both women have done a poor job formulating and implementing education policy and both should go.
'Lacked street smarts'
Massey University education professor John O'Neill said that on paper Mrs Longstone, with her extensive education experience in Britain, was well qualified for the job, but lacked the on-the-ground experience to handle controversial education policies.
Professor O'Neill told Morning Report that Mrs Longstone would have been attractive ideologically to a Government that wants to embark on radical privatisation agendas. "But the reality is that she didn't have the street smarts that are expected of a top-level public servant."