Education Minister Hekia Parata says it is up to her top bureaucrat to decide whether more heads should roll over the Novopay debacle.
The Education Ministry's Deputy Secretary Anne Jackson announced her resignation yesterday in the wake of the ministerial inquiry into the school payroll system.
A second senior staff member's actions are still being investigated.
Ms Parata would not give an indication today whether there would be another resignation, saying employment matters were entirely up to Acting Secretary for Education Peter Hughes.
"Those are matters and processes and decisions that he is in charge of," she told Radio New Zealand.
"He will advise me of those matters when he feels that is appropriate to do."
Ms Parata said the comprehensive ministerial inquiry had made it clear where the responsibilities lay over eight years.
"It also made it very clear that information represented to me and to ministers was not accurate or reliable at certainly very critical points."
NZEI national secretary Paul Goulter said Ms Parata had not asked the right questions about Novopay.
He told Radio New Zealand it would take more than one resignation to restore teachers' trust in the Ministry of Education and called for her and other ministers to resign.
But Ms Parata took exception to the suggestion she did not ask the right questions.
"I can say absolutely that I did ask the appropriate questions at every juncture," she said.
"The report makes it clear that the answers and assurances that we were given were either overly optimistic or inaccurate or misrepresented, and if you're making decisions relying on the information you're given and the information is wrong, then the decisions are going to accordingly also be affected by that."
Ms Jackson yesterday said the report had identified shortcomings in areas for which she was responsible as deputy secretary of schooling until July 2012.
"As a result, I have decided to tender my resignation. I hope my resignation will help the ministry put the Novopay issues behind it. I am truly sorry for the extra pressure and stress put on teachers, staff and pay administrators during its introduction."
Ms Jackson said the decision to resign was hers alone, and there was no pressure put on her.
Her resignation follows that of former Secretary for Education Lesley Longstone as a result of a poor working relationship with Ms Parata.