Victoria's "tough" border policy will stand despite thousands of residents languishing in NSW limbo.
Police Minister Lisa Neville confirmed the number of exemption applications had risen to 2798 by Tuesday, as the state reported all three new locally acquired cases were linked to the 27-strong Black Rock cluster.
Just 57 exemption requests have been granted to date, while another 153 cases were told they didn't need to apply as they were emergency workers or required urgent medical care.
The plight of Victorians stranded across the NSW border was among COVID-19 matters discussed by Premier Daniel Andrews with Prime Minister Scott Morrison on Monday night.
In a radio interview on Tuesday morning, the prime minister said the federal government was willing to provide support "to get a better pathway home for Victorians as soon as possible".
But Ms Neville, fronting the media as Mr Andrews continues his leave, said there would be no change to the exemption policy.
"I understand it causes hardship for people," she told reporters on Tuesday.
"There is a tough exemption process to pick up those who are facing the hardest hardship.
"But otherwise we've had to make this decision to protect what we've all built together. We don't want to go backwards."
Former federal Labor leader Bill Shorten revealed a mother of an 11-year-old child with disability has contacted him in a bid to expedite the Victorian family's return from the NSW south coast.
He said the exemption system "doesn't seem to be working the way it should" and implored Victoria's Department of Health and Human Services to speed up the assessment process, which is taking up to 48 hours.
Ms Neville said additional DHHS staff have been allocated to respond to the deluge of applications, although couldn't give a timeline for when she expected the backlog to be cleared.
Last Friday's sudden border closure has forced some desperate returnees to take extraordinary steps in an attempt to illegally cross Victoria's 32 NSW border checkpoints.
Assistant Commissioner Rick Nugent said Victoria Police had turned away 1532 motorists trying to enter the state, issuing 1232 warnings and 50 fines.
Those fines were meted out to border motorists with non-border occupants in their vehicle, for "checkpoint shopping" and misleading permit applications.
Mr Nugent said a couple said they had been to a closed local restaurant across the border, only for police to find a receipt in their car for a northern Sydney takeaway store.
"They'd just driven directly from there and tried to enter into Victoria," he said.
From 32,544 tests on Monday, Victoria recorded three new locally acquired coronavirus cases along with another in hotel quarantine.
All three local cases are connected to the Buffalo Smile Thai restaurant in bayside Melbourne and linked back to Sydney's northern beaches cluster in NSW.
The latest round of exposure sites to be added or updated include the Sikh Temple in Keysborough, Springvale Shopping Centre and its IKEA store, Bodriggy Brewing Company in Abbotsford and Merrymen Cafe in Hampton.
They are among 19 sites linked to the Black Rock cluster where anyone who has visited at specific times must be tested immediately and quarantine for 14 days.
More than 1000 primary and secondary contacts were isolating as of Monday.
