The Secondary Principals Association is seeking legal advice about compensation for schools affected by problems caused by the new payroll system.
Some 90,000 staff should have been paid in the first cycle of the web-based Novopay system on 5 September, but more than 5000 were underpaid and at least 55 people not paid at all.
A helpline has been inundated with calls from unhappy teachers.
The association's president, Patrick Walsh, told Radio New Zealand's Checkpoint programme on Wednesday that schools want compensation to pay the cost of dealing with the mistakes.
"We are speaking with the lawyer that represents secondary school principals in New Zealand and we'll take his advice on whether the schools involved with Novopay would be entitled to some form of compensation."
Mr Walsh says principals report they are spending a lot of time dealing with upset and stressed teachers, and compensation will be sought from the Ministry of Education or Novopay.
The Principals Federation supports the move. President Paul Drummond says dealing with the errors has taken goodwill from the sector.
Mr Drummond says he has suggested to the Ministry of Education that it set up a mechanism to allow schools to make claims for extra costs incurred.
However, the ministry says it has not received the proposal, so can't consider it.