Anyone who has arrived from Perth in recent days is being asked to check locations of interest of the latest cases, and monitor their health.
At this stage Perth has avoided moving into a lockdown, though Mark McGowan mentioned there will be an update on this tomorrow morning.
New Zealand health officials today participated in a meeting with their Australian counterparts to further assess the public health risk of the recently identified COVID-19 community cases in Perth.
New Zealand's tourism industry was its biggest export industry before COVID-19, with Australians accounting for about 40 percent of the worldwide visitors.
Around 750 passengers who travelled either directly or indirectly between Western Australia and New Zealand between 27 April and 1 May are being contacted today by the Ministry of Health's contact tracing team and being given the above advice.
"I want to avoid going into lockdown again - I know how much it can impact people's lives and businesses - but if we need to go back into lockdown we will", he said.
No cases have been reported in the Cook Islands since January 3.
An Air NZ flight and a Singapore Airlines flight from Perth were both cancelled overnight, after revelations a security guard had tested positive at a Perth MIQ facility.
Director-general of health Dr Ashley Bloomfield said while the public health risk was low, we must remain vigilant as we enjoy the opportunities quarantine-free travel had provided.
The Ministry of Health will provide another update about the situation regarding Western Australia on Sunday.
The premier said he would not place the state into another lockdown, and instead revealed masks would still be required by those in the city and the Peel region.
And it says 27 out of 397 passengers who arrived in New Zealand from Brisbane after an airport cafe "green-zone breach" are now self-isolating.
To date 27 people have got in touch with Healthline to say they were in the locations of interest at the relevant time.
These passengers are considered casual plus contacts and must self-isolate and get tested five days after the exposure.
The call to pause flights came after a hotel quarantine security guard and two of his seven housemates in Perth were identified as having tested positive for Covid-19 on Saturday night.
He added the risk was low given the nature of food delivery work typically being low contact, as well as the community "being in a state of semi-lockdown" during the period they were potentially infectious.
The hotel quarantine worker, aged in his 20s, is believed to have been infectious in the community for four days, during which time he visited a number of locations including a shopping centre and a Coles.