The up to 17 people detained when trying to enter Melbourne after flying in from New Zealand have not yet reached out for consular help.
The passengers are reported to have flown into Sydney under a new travel bubble with New Zealand and then taken a connecting flight to visit family in the state of Victoria.
However, those detained had not approached the Ministry of Foreign Affairs and Trade "for consular assistance", a spokesman said.
Victoria is not accepting overseas arrivals at the moment and the arrival of the travellers sparked an outcry from Victorian health authorities for allowing them to slip through.
Victoria's Department of Health and Human Services confirmed it did "not have legal authority to detain the travellers on arrival".
"Victoria has not agreed to a travel bubble arrangement with New Zealand and did not expect to receive international travellers as a result of NSW making that arrangement," DHHS said.
"The Victorian Government has made it clear to the Commonwealth that we expect NZ passengers who have not undertaken quarantine will not be permitted to board flights in Sydney bound for Melbourne."
The Australian Border Force said "domestic border restrictions are a matter for states and territories".
The statements left it unclear exactly where the travellers were being detained.
They had earlier been allowed to travel to Sydney without quarantining, as part of a trans-Tasman travel bubble.
Under the deal between the two nations, New Zealanders will be allowed to travel quarantine-free into NSW and the Northern Territory if they have not been in a Covid-19 hotspot in the previous 14 days.
Reaction on social media was swift.
"Why anyone would come to melb at this time I don't know," wrote another, in reference to the months-long Covid-19 restrictions in the city, after it was affected by a severe second wave of the virus.
Another was more welcoming, posting "Welcome to Hotel Melifornia."
Earlier on Friday afternoon, Morrison said about 230 New Zealanders had arrived in Sydney.
"We have already welcomed our first Kiwis back to Australia for a holiday. That's fantastic," the Prime Minister said.
"Some 230, I understand, were on the flight this morning that has arrived, and I think is just going through customs now as we speak, and there are others who will be coming."
"We welcome those Kiwis, Kia Ora to those Kiwis who've joined us today, I hope you enjoy your holiday in New South Wales or the Northern Territory or the ACT and tell your friends and we're looking forward to seeing more of you."