PSA organiser Will Matthews said the union has maintained the strikes would be deferred if the DHBs came to the table with a better offer, or in the event of a public health emergency.
He said striking is a last resort and implored the DHBs to recognise the hard work and sacrifice of its staff by coming up with a fair pay deal.
"Striking has always been our last resort, and our members in Auckland continue to demonstrate their commitment to providing quality health care to New Zealanders by working tomorrow."
District Health Boards (DHBs) welcomed the Employment Court's ruling to stop Friday's strike.
DHB spokeswoman Keriana Brooking said the current Omicron outbreak is putting "extraordinary pressure" on DHBs.
"We're glad the PSA responded to the request from the three DHBs in Tamaki Makaurau and had already called off the strike in Auckland."
Brooking said they will have facilitation with the Employment Relations Authority early next week to focus on ways to help settle the pay talks.
"The PSA has told us Pay Equity is the real concern of its members – that's a completely separate process and our aim is to settle these pay talks so we can concentrate on that," Brooking said.
The strike planned by Allied Health workers could have seen a number of hospital, community and outpatient services postponed.
Allied health covers a broad range of services including, physiotherapists, laboratory workers, speech and language therapists and social workers. The nationwide action covers 10,000 PSA members.
Meanwhile, Canterbury and West Coast DHB Chief Executive Dr Peter Bramley said he was pleased there will be no further disruptions. However, the DHB acknowledged some appointments or surgery had to be deferred before his ruling.
"We respect the right of our staff to take industrial action and acknowledge the important role that all health workers play in delivering high-quality care, but I am pleased we're able to continue to provide treatment and care without further disruptions for our community at this time," he said.
Matthews is encouraging Health workers to picket during their lunch break.
"Our nationwide digital picket will also continue from 11.30am-1pm, and we encourage our Auckland members to call in to this on their lunch breaks."
A new date for the protest has been scheduled on March 7 and 8.