Two travellers from New Zealand have been forced into COVID-19 quarantine after unexpectedly arriving in Queensland.

Deputy Premier Steven Miles said the pair flew from Sydney and have been placed in mandatory hotel isolation.

“There are currently two people in hotel quarantine in Queensland who travelled from New Zealand under the arrangements made by the Morrison government,” he said on Tuesday.

Mr Miles said there had been “no further consideration” about the Sunshine State joining the travel bubble with New Zealand.

Since Friday, New Zealanders have 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.

Until Tuesday no other states had given the go-ahead for tourists but that did not stop New Zealanders flying on to Melbourne, Perth, Adelaide and Hobart.

Victorian Premier Daniel Andrews has lashed out about being included in the bubble, despite specifically requesting not to be, and Western Australia has also asked to the federal government to do more to brief states about incoming Kiwis.

But federal Tourism Minister Simon Birmingham said the spat served only to expose the inflexibility of domestic quarantine rules.

He called on South Australia, in particular, to reconsider its coronavirus restrictions.

“I think that is a very, very strong ground for South Australia to think about joining NSW and the Northern Territory in allowing New Zealanders free entry to SA,” he told ABC radio on Tuesday.

“I hope that we will see, pretty soon, New Zealand to reciprocate for states like South Australia that have done just as well as New Zealand, in terms of managing COVID.”

South Australian authorities were quick to heed his calls. The state government announced early on Tuesday afternoon that it had dropped its opposition to the travel deal, and would immediately open its borders to NZ travellers. Twelve recent arrivals who were sent into quarantine were allowed into the the community.

Police Commissioner Grant Stevens said South Australia would also be “happy to accommodate” direct flights from New Zealand.

New Zealand Prime Minister Jacinda Ardern says the walkabout Kiwis are a matter for its state and federal governments. She encouraged Kiwis to check the rules but stopped short of scolding her wandering citizens.

“From our perspective, 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.

“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 has said it will do the same only when several criteria are met – principally a run of 28 days without local transmission of the virus in Australia.

New Zealand recorded its 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. NZ health officials believe he picked up the virus on the Sofrana Surville, which is 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.

-with AAP