NZEI president Lynda Stuart said teachers would vote on the offer by an electronic ballot run by Elections NZ between September 18 and 25. Union negotiators are not making any recommendation for or against it.
A vote to accept the offer will end the dispute, but of the vote goes against it, the NZEI will discuss its next steps at its annual conference in early October.
Teachers who attended rallies in a national one-day strike on August 15 have already indicated in straw votes that they would support a further two-day national strike if necessary.
Stuart said beginner teachers had already made it clear that they wanted a flat pay rise for everyone rather than a bigger increase for themselves.
"They wanted to see that offer being across the board so that they could see the map of their career," she said.
She said the union also wanted action on staffing, such as a reduced teacher/student ratio in Years 4 to 8 and funding for special needs coordinators. The ministry's latest offer does not include anything new on those issues.
"We know that everything can't happen at once, so we have been really clear around the importance of being able to stage things," Stuart said.
"We know there is a teacher shortage so we are not going to be able to do everything that requires extra staffing all at once. We have been having those conversations when we are in the [negotiating] room."
NZEI's teacher lead negotiator Liam Rutherford said members would "consider whether the offers addressed the needs of children and their learning".
"It also remains to be seen whether parents and the wider public think the offer would make a difference for children," he said.
"As teachers and principals we can see that the issues in our schools simply can't wait any longer and our students' learning is already being negatively affected because of the difficulty in recruiting and retaining teachers.
"Member leaders are not making any recommendation to the wider membership about whether to reject or accept the offer."
Ministry of Education head Iona Holsted said the new offer "responds to the union's concerns the first offer was too heavily weighted towards new teachers, and increases the quantum".
"It provides a cumulative increase of 9.3 per cent over three years; to teachers a 3 per cent increase for all teachers each year, over the next three years," she said.
"The first increase will take effect when the collective agreement is settled, the second increase 12 months later and the third 24 months later.
"The cost of the ministry's offer for teachers and principals is $569 million over four years."
