Defence Minister Linda Reynolds has accused the Victorian government of rejecting offers for troops to help with hotel quarantine.
The bungled regime has emerged as a flashpoint in souring relations between the Morrison government and its Victorian counterparts as the deadly outbreak rages.
Victorian Premier Daniel Andrews told a parliamentary inquiry Australian Defence Force personnel were not offered to the state government.
"I don't believe ADF support was on offer,'' he said.
"It is fundamentally incorrect to assert that there were hundreds of ADF staff on offer and somehow, someone said no."
Senator Reynolds contradicted him, saying Victorian authorities advised the federal government in late March no help was needed with hotel quarantine.
"The ADF was consistently advised that its assistance was not required for any public-facing roles in Victoria," she said.
"ADF officials asked whether Victorian authorities required assistance with its mandatory quarantine system on multiple occasions.
"No request for quarantine support was subsequently received from Victoria at that time."
Australia's death toll is 331 after a second consecutive day of a record 19 coronavirus deaths in Victoria.
Breaches in hotel quarantine are believed to be behind the second wave, which has put the state into the nation's harshest lockdown.
Senator Reynolds said on April 12, state authorities reaffirmed to the ADF that Victoria was capable of monitoring compliance.
Mr Andrews said the ADF only transported people from the airport to hotels in NSW.
But the defence minister said ADF personnel undertook compliance monitoring at hotels in NSW.
Senator Reynolds said troops had also supported quarantine arrangements in Queensland.
Acting Chief Medical Officer Paul Kelly said the nation was still performing well internationally, despite the tragic deaths.
He said the average age of people who had died nationally was well over 80, with many victims aged in their 90s.
"Our death rate within the total 21,000 cases we have had is extremely low and there have been very few cases outside of aged care," he said.
"It's a tragedy to lose a loved one but really, there have been very few deaths in comparison to other countries."
Australian Associated Press