Scott Morrison is under increasing pressure to bring more stranded Australians home from overseas.
With international borders set to remain closed for the rest of this year, there are growing concerns about Australian expats in precarious positions.
There are still more than 38,000 citizens overseas who are desperate to return.
Labor senator Penny Wong accused the prime minister of outsourcing responsibility for stranded Australians to the states.
"The roadblock is Scott Morrison's stubbornness in refusing to discharge his responsibility for national quarantine," she told ABC radio on Wednesday.
"Quarantine is a federal responsibility. We need a safe national quarantine system.
"But we've got a 'I don't hold a hose, mate' moment from the prime minister who stubbornly refuses to step up and is handballing the issue."
The federal government has organised more than 20 chartered flights over the next few months to cut down the number of stranded Australians.
Senator Wong argues that is too little, too late.
"But more importantly, flights are not the primary blockage, the primary blockage is quarantine," she said.
"If we have more quarantine, we can then arrange more flights."
The issue has also been inflamed by the arrival of international tennis players for the Australian Open.
Tennis Australia has arranged 17 flights for 1200 foreign players and officials in just the past few weeks, and found them additional places in hotel quarantine.
By contrast, critics have accused the prime minister of running a "government-run lottery" and "compassion competition" for Australian citizens returning home.
Work is being done on alternatives to hotel quarantine, which will be presented to national cabinet later this week.
Queensland will take to Friday's meeting a proposal to use a mining camp for quarantine.
Mr Morrison is open to the idea, noting similar arrangements are already in place at Howard Springs in the Northern Territory.
He acknowledged there would be "understandable anxiety" in regional communities about how the proposal would work.
"Those issues have to be worked through, we had to do that in Howard Springs but that worked, and so we will just take it step-by-step," Mr Morrison told 2GB radio.
"I'm always happy to hear good ideas."
Chief Medical Officer Paul Kelly has warned international border restrictions are "probably going to be one of the last things to change rather than the first".
But Professor Kelly said work was well advanced on how international travel could be gradually reopened.
He said the travel bubble with New Zealand proved international travel could be done safely, but the situation was being carefully monitored before other "green zones" were declared.
Professor Kelly said despite no other suitable country yet being found, there were some that were very low risk.
"We are definitely open to other bubbles."
