If members did reject the offer then possible industrial action would be discussed, he said.
"Us standing still is us standing backwards. We are very disappointed at the offer and it won't make a difference for us to move forward," Rutherford said.
Workload issues had also been largely ignored, as had the request to fund a Special Education Needs Co-ordinator (SENCO) in every school, to assist children with additional learning needs.
"There wasn't anything in the offer that supported the need for a specialised role."
It was "genuinely up to the members" to reject or accept the offer, he said.
Union meetings to discuss the pay offer would begin soon, the first at the Vodafone Events Centre in Manukau on June 18.
MoE deputy secretary early learning and student achievement Ellen MacGregor-Reid said the ministry had put a fair offer on the table and would continue to negotiate in good faith.
"To attract new teachers the offer will see a cumulative increase of 14.7 per cent to base salaries for graduates with a teaching degree ($47,980 to $55,030) over three years, and a 14.2 per cent cumulative increase for graduates with a subject degree and graduate teaching diploma ($49,588 to $56,638) over three years.
"Teachers on the next steps (6-11) will see a cumulative increase of between 6.5 to 13.7 per cent to base salaries over three years. Teachers on the maximum step (12) will receive a cumulative increase of 6.1 per cent over three years ($75,949 to $80,599.)"
MacGregor-Reid said the ministry was working with the sector to develop a workforce strategy to improve recruitment and retention as well as "engaging with the profession on a major education reform programme that includes the development of a learning support action and plan".
"The strategy also includes looking at assessment, which teachers have told us impacts on workload and their ability to focus on teaching. The Government has already removed National Standards in response to teachers' claims it was a large driver of workload.
"Last month's Budget included another $20 million to address teacher supply, $272m additional funding for learning support, $59m for teacher aides, and $394m for new schools and classrooms."
Meanwhile for nursing union members two -hour strikes looked likely after the New Zealand Nurses Organisation said it was "distressed" and "disappointed" with DHBs' revised pay offer.
And retail workers in Auckland planned to picket on busy Queen St tomorrow over pay and performance conditions.
Auckland Farmers workers wanted the company to phase out its performance pay system, which they claim held down wages, and asked for workers to be paid a living wage, FIRST Union retail, finance and commerce secretary Tali Williams said.