The Morrison government has ruled out concerns Australia's Pfizer supplies could face a shortfall next month.
Victorian Premier Daniel Andrews said last week's national cabinet meeting of federal, state and territory leaders was told about a potential issue.
"I don't know how big the problem is, but there is an issue with Pfizer vaccine supply in October," he told reporters in Melbourne on Monday.
"That is not the federal government's fault. I'm not blaming anyone, I'm just making a point."
But federal Health Minister Greg Hunt said the problem, which involved the timing of one shipment, had been solved over the weekend.
"We're expecting all of our contracted anticipated deliveries will arrive in full," he told reporters.
Mr Hunt said Australia would go from 10 million doses of mRNA vaccines Pfizer and Moderna received this month to more than 11 million in October.
"Every state and territory is receiving their full allocations," he said.
ACT Chief Minister Andrew Barr wants more doses for state and territory-run vaccination hubs rather than general practices and primary health networks.
Mr Hunt said GPs had been the backbone of Australia's rollout.
"Whether somebody is vaccinated in a state clinic or a Commonwealth clinic, whether they're vaccinated in a GP or a pharmacy, what matters is that they're vaccinated," he said.
Moderna started arriving in states and territories on Monday after the first shipment touched down last week, with pharmacies the main administration point.
Australia has fully vaccinated 47 per cent of its population aged 16 and above, while 72 per cent have received a first dose.
The ACT leads the nation on double-dose coverage with 56.3 per cent, ahead of NSW at 53 per cent and Tasmania at 52.2 per cent.
Victoria and South Australia have vaccinated 44.1 per cent of over-16s while Queensland and WA are on 41.8 per cent.
The NT has a 47.8 per cent two-dose vaccination rate.
Victoria recorded 567 new cases and another death on Monday.
NSW reported four deaths and 935 new local cases, the state's lowest daily infection increase since late August.
There were seven new cases in the ACT, the first single-figure rise for almost a month.
Darwin recorded one new local coronavirus case in a man who returned from NSW via Brisbane.
While 24 close contacts have been forced into two weeks isolation, the NT government has decided not to impose a lockdown because he went straight from the airport to quarantine.
Australian Associated Press