To date, 27 people have been in touch with Healthline to say they were in the locations of interest - a coffee shop and public toilet - at the relevant time.
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.
Earlier it was announced Perth had avoided a lockdown.
The Ministry of Health says flights from Western Australia to New Zealand should be paused, after more Covid-19 cases were identified in Perth.
"Currently we understand about 20 people were also in that class and they have been contact or are being contacted as we speak, so they can be tested and put into isolation", he told reporters.
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.
Air New Zealand's flight due to leave Perth late last night was cancelled. "We'd like to thank people for their patience and cooperation".
Today's update comes after flights from Perth to New Zealand were suspended following the announcement yesterday of three new Covid-19 community cases across the ditch - a security guard at a Perth quarantine facility and two household contacts.
Meanwhile, 27 travellers who were at Brisbane Airport when two red zone travellers entered the green zone have been asked to get tested for Covid-19.
Despite no new cases being detected today, Mr McGowan is refusing to rule out a stricter lockdown in the days ahead.
Contact tracing teams have identified there were 397 passengers aboard the three flights which left Brisbane International Airport after the green zone breach on Thursday April 29.
A hotel quarantine security guard and two of his housemates tested positive for Covid-19 in Perth on Saturday. The man had worked at the Pan Pacific Perth, and may have been infectious in the community since April 27.
The ministry said Western Australia health officials were meeting to decide whether they would implement further restrictions or a full lockdown.
The country could also benefit from setting up a facility similar to the Northern Territory's Howard Springs quarantine hub which hasn't had a single coronavirus case leave its walls, the university researchers said.
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.
These passengers are considered casual plus contacts and must self-isolate and get tested five days after the exposure.
The case from Japan is a contact of another pre-existing case, while the others were found during routine testing in managed isolation.
A reminder for people who may need a COVID-19 test - please visit Auckland Regional Public Health Service (ARPHS) for all testing locations in Auckland.