NZNO had about 1200 members in Northland alone, including nurses, hospital midwives and healthcare assistants.
Governor said many nurses were angry and disappointed with the panel's recommendations.
"If you look at the social media, they're mostly looking (for) the 18 per cent mark."
One issue was understaffing, which resulted in longer hours and difficult working conditions.
"It's looking like there's still going to be strike action."
The new offer included a $2000 lump sum and an increase in on-call rates from $4.04 to $8, and from $6.06 to $10 for public holidays.
There would also be an immediate 2 per cent investment in additional nursing staff to ease pressure on existing staff.
The offer would also add two steps to the top of the registered nurses' pay scale, which DHBs' spokeswoman Helen Mason said would mean some nurses would earn significantly more.
"Nurses have used teachers as a benchmark - this offer moves their base pay rates to a similar level, with penal rates lifting average earnings of a registered nurse with five years' experience to $93,000, moving them even higher," Mason said.
The DHBs previously offered a 2 per cent annual salary increase in March, along with a $1050 lump sum and a commitment to a pay equity settlement in July next year.
Nurses' starting salaries were around $49,000 a year, the NZNO website says, with a top salary of $66,755. Senior nurses and midwives earn more.
The union wanted nurses to have parity with teachers, who also studied three-year degrees.
The strike action would run for 24 hours from 7am on each of the two days, July 5 and 12.
DHBs were expected to put contingency plans in place for a strike, which would likely include cancelling elective surgeries, Governor said.
"It's up to the DHBs to manage and to do their contingency plans."
Governor said strike action was not something nurses took lightly, despite the current support for industrial action.
"For staff to walk away from their patients, it's a very hard thing to do."
NZNO chief executive Memo Musa said the union was meeting DHB representatives to prepare for industrial action.
Northland DHB was approached for comment, but did not respond by deadline.