Post Primary Teachers’ Association (PPTA) members voted to reject the new offer and for a partial strike from Monday to Thursday.
Union members would refuse to teach, instruct or supervise students in certain year levels on specific days.
The industrial action will affect year 12 and 13 students on Monday, year 11 on Tuesday, year 10 on Wednesday and year 9 on Thursday.
PPTA Otago regional chairman Kussi Hurtado-Stuart said the situation was "really frustrating" as it was during a "critical" point in the year when students were preparing for exams.
The government’s offer, as far as the union could tell, was "a pay cut rather than a pay rise", he said.
"Being put in the position where you get a second offer that’s still below inflation ... is frustrating.
"Our executives have made our position very, very clear, and they’ve told the negotiating team from the Ministry of Education that members are unlikely to accept this offer.
"It feels a bit like a waste of time to go through this process, just like last time when we were offered 1%."
There was still a lot the government had not yet considered, Mr Hurtado-Stuart said.
The union wanted all of its other non-pay conditions to be addressed — including in-classroom support, allowances for correspondence school Te Aho o Te Kura Pounamu and an increase in payments for management units.
Teachers were trying to look after their students as best as they could, while making sure they did not breach the strike conditions, he said.
The partial strike action would only be for about six hours each day, meaning its members could still supervise after-school sports and before-school activities.
Everyone would be back at school on Friday, Mr Hurtado-Stuart said.
The new offer included consecutive pay rises of 2.5% and 2.1% over two years for teachers at the top of the pay scale, compared with the previous offer of three 1% rises over three years.
Public service commissioner Sir Brian Roche said the union was choosing strikes over students and urged it to return to the bargaining table.
The offer on the table was strong, fair and addressed cost-of-living pressures without ignoring the fiscal pressures facing the country, he said.
It represented a pay increase of 4.7% within 12 months for secondary teachers already at the top of their pay scale.
