A Herald report on September 1 revealed inconsistencies between hospitals' visiting rules under alert level 4.
While other hospitals were only letting visitors in on compassionate grounds, Auckland DHB's policy allowed each patient two visitors, one at a time.
These apply for Auckland City Hospital, Starship Children's Hospital and Greenlane Clinical Centre.
Visitor information on the Auckland DHB website says people are screened on arrival and those with cold or flu symptoms are not allowed to enter.
NZNO wants visitor access to be restricted to compassionate grounds and only when absolutely necessary during the current Delta outbreak, in line with those of other District Health Boards across the Auckland region.
Wait says the Auckland District Health Board refused to meet for mediation Friday.
They had a Zoom meeting with ADHB lawyers and the Employment Relations Authority on Saturday, and the parties were directed to engage in urgent mediation.
NZNO proposed the mediation take place on Sunday but ADHB has refused to meet before Monday afternoon.
A hearing is set with the Employment Relations Authority on Thursday if they can't reach agreement.
Wait says the delay is allowing further time for unnecessary close contacts to occur.
"We urge ADHB to engage with us without delay, and to stop putting the health and safety of our members and the public at risk."
WorkSafe had issued an improvement notice directing Auckland DHB to engage with its workers on the policy, and a union health and safety representative had done similar but Wait says the voices of workers have largely been ignored.
"It's staggering that we should have to appeal to a higher authority just to get them to talk to us about what is clearly a sensible and appropriate health and safety measure at a time of serious public danger," he said.
In a statement, Alex Pimm, incident controller at Auckland DHB said: "We believe that whānau are an important part of a patient's care, treatment and recovery and have therefore enabled access to whānau for patients in our care.
"We believe we have done this in a way that minimises risk to other people on our sites."