New Zealand health officials met their Australian counterparts on Sunday to assess the public health risk of Perth's new community cases - concluding that the risk to public health in New Zealand was low.
The ministry said it had advised airlines that flights between Perth and New Zealand could resume as early as Monday.
However, anyone in Australia - including Kiwis - who had been at a location of interest could not travel to New Zealand within 14 days of the exposure.
This would include any future locations of interest determined in the coming days, health officials said.
Anyone who had been in Perth since April 27 is advised to check the Western Australian Government website for locations of interest and advice regarding isolation and testing.
Anyone who had recently arrived in New Zealand from Australia who had been in a location of interest at the specified time should self-isolate immediately and call Healthline.
Around 750 passengers who travelled between Western Australia and New Zealand between April 27 and May 1 were being contacted by contact tracers and advised what to do next.
Director general of health Dr Ashley Bloomfield said the public health risk was low, but New Zealand must remain vigilant as it enjoys the opportunities quarantine-free travel had provided.
"There are some additional public health measures we require of people who are or have recently been in Western Australia."
In Western Australia, a number of restrictions had remained in place since the Perth and Peel regions emerged from lockdown roughly a week ago, including mask-wearing, limits on indoor and outdoor gatherings and a ban on visitors at aged-care facilities and hospitals.
McGowan said the state was able to avoid a lockdown this time based on the restrictions that had been in place over the past week.
"It has significantly reduced the risk of transmission in our community."
About 20 people had been identified as close contacts of the infected trio - 16 had so far returned negative results, the Premier said.
Air New Zealand spokesperson said the airline would operate its quarantine-free Perth to Auckland service on Monday with NZ176.
Check-in teams at Perth Airport would ask passengers additional screening questions before they would be accepted for travel.
Passengers that had been at one of the locations of interest in Western Australia between April 17 - 23 and April 27 – May 1 would need to self-isolate for 14 days from the time of exposure before travelling to New Zealand.
Meanwhile, nearly 60 per cent of the 4000-odd eligible Air New Zealand crew members had received both doses of their Covid-19 vaccine since February, the Ministry of Health said.
Eligible staff members included those recently rehired for the transtasman travel bubble, as well as cabin crew, pilots, airport, cargo and line maintenance employees in Auckland and Christchurch.
The Covid-19 vaccine is only mandatory for crew members on managed isolation and quarantine (MIQ) flights – a rule that came into effect at midnight on Friday.
Meanwhile, the Ministry of Health provided an update on Sunday on the Brisbane International Airport green-zone breach, where two red-zone passengers used spaces reserved for green-zone passengers.
Contact tracers had identified 397 passengers across three flights that had left Brisbane International Airport after the breach, of which 27 had been in touch with Healthline and advised to self-isolate.
Two people were yet to be contacted and attempts to reach them were ongoing, the ministry said.
Four new MIQ cases were announced in New Zealand on Sunday but no new community cases were reported.
Two of the cases were from Qatar, one each from Japan and Pakistan.