Primary and intermediate school principals have rejected the government's latest pay offer, because it does not give them the same pay as secondary principals and leaves some earning less than senior teachers.

The decision follows more than a year of bargaining that has included three strikes in combination with primary school teachers, who have voted to accept their offer.

The Educational Institute announced the ballot results this morning.

The union's president, Lynda Stuart, says it had recommended principals accept the offer but they rejected it in part because the teachers' deal provided pay parity with secondary teachers but the principals' offer did not.

She says the offer also did not resolve the problem of senior teachers and managers being able to earn more than the principals of small schools.

"Principals historically are paid according to the size of their school. That doesn't take into account the complexity of the role of the principal," she says.

"We've got principals who are saying 'actually, I might as well leave this small-school role and go and be a deputy principal elsewhere'."

Lynda says the union wanted the minimum pay rates for principals at schools with between one and 50 children and schools with 51-100 children raised to the same level as principals of schools with 101-150 pupils.

Louise Green, from the union's bargaining team, says primary principals were paid two per cent less than secondary principals and they wanted pay parity.

"If we say a teacher is a teacher no matter where they are - whether they're in early childhood, primary or secondary school - then the same for ... the principalship," Louise says.

The Education Ministry said there were 267 U1 principals and 244 U2 principals and it had offered them pay rises totalling 14 percent by July 2021.

Secretary of Education Iona Holsted says the ministry was disappointed principals had rejected a "substantial" offer.

Iona says the ministry had agreed to discuss how pay parity would be applied to principals but it was a much more complex issue for principals than for teachers.

"We remain available to meet with NZEI to discuss how the offer could be repackaged within the existing envelope for primary principals," she says.

Currently, the principals of the smallest primary schools earn between $83,873 and $93,757 depending on experience, and the ministry's offer would have increased that to between $95,296 and $105,180 by July 2021.

The offer accepted by primary school teachers would give the union's members pay rises of between $2000 and $4000 on 1 July and would increase their pay by at least 18.5 per cent by July 2021.

It would set a new top rate of pay for primary teachers of $90,000.

The Educational Institute says the teachers' deal was a big win for collective campaigning.

The union expected to announce the results of area school teachers' ballot on their collective agreement on Friday and a ballot of secondary teachers by the Post Primary Teachers Association was due to end on Friday.

-RNZ/John_Gerritsen