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The offer would have left the principals of the smallest schools earning less than senior teachers and managers at larger schools.
However, primary school teachers have accepted their offer, which will increase most teachers pay by about 18 percent over three years.
Earlier in June, RNZ reported that the teachers' unions, PPTA and NZEI, would recommend their members accept the government's new pay offer, which included a one-off $271 million boost to create a unified base salary scale for primary, secondary, and area school teachers.
Education Minister Chris Hipkins said at the time a key element of the revised deal was a unified base salary scale for all primary, secondary and area school teachers and will restore parity between primary and secondary school teachers.
The NZEI, which represents primary teachers and principals, said in a statement said the offer to principals was unchanged from a previously rejected offer.
Union president Lynda Stuart said while primary teachers had won parity with their secondary counterparts, the government did not offer primary principals parity with their high school equivalents.
"That clearly isn't fair, so they have voted to fight on for a better offer."
The union was urgently seeking a return to the negotiating table in order to resolve these problems, and would be consulting with its members, she said.
However, the outcome was "a big win" for teachers who had campaigned alongside principals for 18 months and held three strike days.
"I am so proud of our teachers for their steadfast collective action in this campaign over a very long period of time," Ms Stuart said.
"I also particularly want to thank parents and the wider public - their suport was incredible in this campaign - and their backing of teachers was critical to us achieving the breakthrough we needed."
While teachers did not get everything they wanted, they did make major progress, winning pay parity and a significant pay increase, as well as a commitment from government to address workload problems, she said.
The primary teachers' new agreement will come into force from 1 July, with a three-month delay in the new terms and conditions for non-members. NZEI members will also recdive a one-off pro rata payment of $1500.