Principals Federation president Perry Rush said by the middle of Friday 850 of its members had voted on the proposal, 92 per cent of whom approved.
"This is a really significant message that members are sending the New Zealand Principals Federation and we've now got a job to talk as an executive and to talk to the NZEI and chart a way forward," Rush told RNZ.
Rush said principals were unhappy with the NZEI over three main issues: the union's current focus on pay equity for support staff, lack of progress on workload and wellbeing problems, and last year's collective agreement settlement.
"Principals were very supportive of teachers who did very well out of collective bargaining. Principals went on strike several time for their terms and conditions and there's very broad agreement across primary principals that the union did not enter into those negotiations with the energy that they would have hoped," he said.
Rush said if a new union was set up it would create a similar situation to the secondary school sector, where principals were represented by two organisations - the Secondary Principals Association's union, and the Post Primary Teachers Association (PPTA).
Asked if members might accept a stronger principal-focused division within the NZEI rather than an entirely new organisation, Rush said all options were on the table.
"We're interested in doing better for principals, that's the work of the New Zealand Principals Federation. Principals are not happy, we want to keep an open mind about how we move forward with this.
"The possibility of a bespoke primary principals' union is on the table, we're interested to see what response the union is going to have," he said.
A member of the NZEI's executive team, Mark Potter, said creating a new union would weaken principals' collective voice.
"We are far stronger together, we really are better if we are all acting in unity," he said.
He said there were about 2000 primary and intermediate school principals and the vast majority belonged to the NZEI.
Potter said the union represented teachers, principals and support staff and those groups could support one another in their respective bargaining and campaigns.
He said some principals were frustrated by lack of progress on problems such as workload, but he had spoken also to principals who wanted to stay with the NZEI.
Potter said the majority of the union's principal members had accepted last year's settlement of their collective agreement.
The president of the Educational Institute, Liam Rutherford, emailed its members telling them the Principals Federation's plan "directly threatens" the union's unity and urging them to talk to principals about it.
"If you're in a school, we encourage you to have conversations with other members, especially your principal, about why we're stronger together when campaigning to fix our workload issues and a lack of resourcing for our schools," he wrote.
