New Zealanders have since Friday been able to enter Australia without the need for 14-day quarantine but only for Sydney arrivals intending on travelling in NSW and the Northern Territory.

Other states are yet to give the go-ahead for tourists but that hasn't stopped New Zealanders flying on to Melbourne, Perth, Adelaide and Hobart.

Ms Ardern encouraged Kiwis to check the rules but stopped short of scalding her wandering citizens.

"From our perspective the the safe travel zones that Australia have established really are for them to roll out, monitor and make sure that they are operating on their side," she said.

"What I would say to any New Zealander looking to travel, make sure you understand the requirements on you first before you enter into any port in Australia.

"And remember that no matter where you go, you will be required to quarantine on return."

While Australia has begun to accept Kiwis without need for quarantine, the New Zealand government says it will only do the same when several criteria are met - principally a run of 28 days without local transmission of the virus in Australia.

New Zealand recorded a first community case in three weeks on Sunday.

That sparked fears of a fresh outbreak but in the two days since there have been no further cases.

The infected man is a marine engineer who worked on two ships and health officials believe he picked up the virus on the Sofrana Surville, now off the Queensland coast.

The case was picked up early and officials have moved swiftly to trace, isolate and test the man's close contacts.

Australian Associated Press