More than 25,000 Australians stuck overseas might not make it home for Christmas unless a cap on international arrivals is lifted.
States are under pressure to boost the capacity of their hotel quarantine schemes to allow more people to return.
The federal government has also been challenged to find a creative fix.
Only 4,000 international travellers can enter Australia each week and the majority fly into Sydney.
NSW Premier Gladys Berejiklian has challenged other states to take their fair share of Australians returning from overseas.
"NSW welcomes back around 2,500 people every week, and we know the hotel quarantine system in NSW is managed well, but we're doing so much more than all the other states combined," she told reporters on Monday.
"I just say to other states, I'm sure many of our Aussies overseas wouldn't mind flying into Brisbane or Perth or even Adelaide, and then getting a domestic flight back to their homes."
Labor says the Commonwealth should take responsibility for quarantine arrangements, pointing out federal facilities have been used to accommodate people returning from China and Japan.
NSW Premier Gladys Berejiklian Source: AAP
Opposition frontbencher Kristina Keneally said the Morrison government was attempting to handball its duties to the states.
"If the Commonwealth government is serious about getting stranded Australians home, they need to step up, show leadership and put a plan in place," Senator Keneally told ABC radio.
"It is the Commonwealth's responsibility to assist stranded Australians in the middle of a global, deadly pandemic, who are stuck overseas."
Home Affairs Minister Peter Dutton says lifting the cap on international arrivals would only be possible if the states increased their quarantine capacity. He has also called on Queensland's state border closure to end.
"The number of people that we can bring in through the international ports at the moment is a function of, say for example, the Queensland government or Queensland Health's direction, that people hop off a plane from Los Angeles have to go into a hotel for two weeks," Mr Dutton told the ABC's Insiders on Sunday.
"At the same time, they've got a cap on the number of places that they're making available at those hotels for quarantine.
"So we're working to those restrictions. I would be happy to double the number of people tomorrow if Queensland Health was to relax the quarantine period of 14 days, if that's what the health advice was."
Nationals MP Barnaby Joyce described Queensland's hardline border measures as a sham after American actor Tom Hanks was allowed to enter the state.
Mr Hanks returned to Australia earlier this month to finish shooting a film, quarantining at a Gold Coast hotel with 11 other family, cast members and production staff.
Their entry was approved by the federal home affairs department at the request of the Queensland government.
US actor Tom Hanks was granted federal approval to enter Australia to film a movie in Queensland. Source: dpa-Zentralbild
"It's in stark contrast to people who can't go to funerals, and that's what aggravates me so much," Mr Joyce told the Seven Network.
"We've got the AFL in there first class, we've got Tom Hanks in there, we've got his offsiders in there, but we can't get a person across to see their dad buried."
Deputy Chief Medical Officer Nick Coatsworth acknowledged state authorities were split over whether internal borders should be open.
"That is largely related to risk tolerance and whether one is prepared to allow any possibility of COVID-19 entering into one state," Dr Coatsworth told the ABC.
"We need to have these ongoing border discussions, they're obviously a live issue."
Victoria recorded 35 new cases and seven more deaths on Monday as stage four restrictions began to ease across Melbourne.
NSW recorded four new cases, including three overseas travellers in hotel quarantine.
No new cases were recorded in Queensland.
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