A "huge gap" remains between the $700 million increase in pay offered to primary school teachers and the union's bid for $2.5 billion.
The Employment Relations Authority has described the New Zealand Educational Institute's bid for $2.5 billion more pay for teachers over four years as "completely unrealistic".
Education Minister Chris Hipkins said the authority had described the government's offer of $700 million more over four years as "handsome and competitive".
The Ministry of Education's latest offer is $129 million more than the previous offer made last September.
However, primary teachers and principals have rejected the pay offer, saying their profession is at breaking point.
NZEI president Lynda Stuart said the latest offer still did not address problems with workloads, release and leadership time, and difficulties attracting and retaining teachers.
"There's a real crisis in education at the moment. We're not growing our own New Zealand teachers and we're not keeping our New Zealand teachers," Ms Stuart said.
Mr Hipkins acknowledged that "a couple of hundred teachers" were employed from overseas last year, so that schools could fill staff vacancies.
"The previous government took their eye off the ball - there was a 40 percent reduction in the number of people training to be teachers," he said.
"We've put quite a lot of effort into that in the last 18 months and we're seeing those numbers turning around."
Mr Hipkins said the union's requests for more release time for teachers could not be fulfilled while the teacher shortage existed, because there were not enough staff to cover.
"They're raising some very legitimate issues, but no government is going to be able to address those overnight."
He said the pay offer would provide on average an extra $10,000 a year for a primary school teacher.
Teachers' salaries were "quite competitive with other professions those people might consider going into", Mr Hipkins said.
Ms Stuart said primary teachers wanted pay parity with secondary teachers, but currently received 3.9 percent less.
Teachers have walked out of classrooms twice since August to pursue their demands for smaller class sizes, more resources and an increase in salaries.
Yesterday, NZEI members said they could strike again next month.
However, Ms Stuart said teachers and principles were not "hanging out to strike" and would like to continue with negotiations until the "sweet spot" was reached.