Prime Minister Scott Morrison and Health Minister Greg Hunt have been urged to intervene, as people caught out by the sudden closure of the NSW border remain stranded for another day.
Meanwhile acting chief medical officer Paul Kelly said there could be a risk in funnelling regional travellers through Sydney and Melbourne, where there is community transmission of coronavirus.
Dozens of Canberrans remain stuck at the Victorian border, after their NSW transit permits were quashed by the NSW government at midnight on Friday.
NSW Premier Gladys Berejiklian said she was concerned travellers passing through from Victoria could pose an unacceptable risk to regional NSW communities.
The NSW government is yet to agree to an ACT government plan for police to escort Canberrans with permits back to the territory and is instead trying to force travellers to fly from Melbourne to Sydney, where they would have to quarantine for two weeks.
Canberra MP Alicia Payne has now written to Mr Morrison and Mr Hunt, calling for federal intervention to solve the impasse.
"This is ridiculous. Clearly travelling back to Melbourne and getting on a plane is higher risk than continuing their drive to Canberra," Ms Payne said.
"Andrew Barr has offered common sense solutions. If NSW can't get their act together, then Scott Morrison and the federal government needs to step in."
Prime Minister Scott Morrison urged the NSW and ACT governments to find a compromise.
"I understand that the NSW Premier will be anxious in these circumstances. We certainly don't want to see people stranded. But I would hope between the ACT Chief Minister and the NSW Premier, they might be able to resolve those matters," Mr Morrison said.
Fenner MP Andrew Leigh said it was "truly bizarre" that NSW would not let Canberrans drive through, given federal MPs from Victoria were permitted to drive through NSW to the ACT over the weekend.
"Those stuck at the border are just trying to get home, often after making a mercy mission to help others. These are people who have done nothing wrong, people who may be grieving or in dire need of rest," Dr Leigh said.
"This indecision from the NSW government is not good enough. They need to step up and reach an agreement to get Canberrans home as soon as possible."
Professor Kelly said the border closure was a matter for the ACT and NSW governments.
He acknowledged travellers passing through regional towns could pose a risk to residents.
"I have spoken before about the virus not moving but people moving so if people are infected with the virus they could be a risk to others as they pass through," Professor Kelly said.
However Professor Kelly said it was also risky to send people to COVID-19 hotspots.
"That's a matter for the states that are involved with those borders, as I've said, but I think as a general principle, [it's] not a good idea to get people to go to places of high risk when they don't need to do so. I'm really hopeful that will be worked through in coming days and have a resolution, which avoids that," Professor Kelly said.
Labor senator Katy Gallagher said if politicians were permitted to drive through NSW, Canberrans should be allowed to as well.
"Politicians had a similar problem, they were due to come through NSW on the weekend, but those problems were fixed almost immediately and people did move through NSW, got their way to Canberra to self-quarantine for parliament," Senator Gallagher said.
"So, you know, it does happen, it's just not happening for this group of people."