National secretary Erin Polaczuk said bargaining teams were shocked and deeply disappointed at the employers' defiant take-it-or-leave-it attitude.
For union members, striking was the last resort.
Disputes could be resolved if employers will come back to the table ready to seriously consider the PSA's offers, she said.
Nurses decided earlier this month to walk off the job next month.
Nurses, midwives and healthcare assistants covered by the Nursing Organisation's collective agreement have issued a strike notice for 24 hours starting 7am, on July 5.
There is also notice for a second, 24-hour strike from 7am on July 12.
New Zealand Nurses Organisation members voted to reject the DHBs' revised pay offer of 9 per cent for all member nurses by August 2019.
The offer equated to $500m.
Health boards were continuing to make contingency plans to ensure emergency and essential services were available if the strike went ahead, DHB spokeswoman Helen Mason said.
"We will continue to do everything we can to settle this agreement and avoid strikes."
Mason said the health boards had worked with the nurses' organisation in the contingency planning process.
Also, New Zealand Educational Institute (NZEI) teachers have voted to accept the Ministry of Education's pay offers or take industrial action.
Teachers and principals were asked to vote on whether a nationwide half-day work stoppage should take place from 1.30pm to 4.30pm on 15 August so members could attend union meetings. It would also mean schools would close for a half a day.
Voting will occur by secret ballot at the paid union meetings of primary, intermediate and kura teachers and principals between 18 and 29 June.
In a bid to urgently resolve the dispute the two parties asked for urgent mediation by the Employment Relations Authority.
Mediation between the two groups ended on Monday without agreement on a revised offer.
The ERA could recommend a settlement.
However, the industrial action looked likely according to NZEI Te Riu Roa lead negotiator Liam Rutherford.
"I haven't met a single teacher that said 'oh yeah I think the offer's about right' I don't think I'll be too far out of line saying that the offer falls well short of what's needed to value teachers," he said.
"We're currently at a point where the teacher shortage we have across the country is at crisis point."
The outcome of the vote would be released on July 14.