Australia is trying to contain a third wave of infections that has locked down its two major cities, Sydney and Melbourne, and its capital Canberra, putting more than half its 25 million population under strict stay-home restrictions.
The federal government has pledged more freedom of movement once 70-80% of the population aged over 16 is vaccinated.
The government agreed vaccine swap deals with Britain and Singapore last week for a total of around 4.5 million doses of the Pfizer-BioNTech vaccine, double this month's supply.
"There will be another set of flights in a couple of days, but we'll pretty much be getting a million of the four million every week over the next four weeks," Lieutenant General John Frewen, head of the vaccination taskforce, told broadcaster ABC.
Frewen said one million doses of Moderna will also reach Australia in "a week or so", becoming the third vaccine to join the rollout along with Pfizer and AstraZeneca shots.
Just over 38% of Australia's adult population has been fully vaccinated, with the country expected to reach 70% by early November based on current rates.
Victoria state, which includes Melbourne, reported 246 new cases on Monday, its biggest daily rise of the year. Daily infections in New South Wales, the worst-affected state, are hovering near record levels.
Despite the recent outbreaks, Australia's coronavirus numbers have remained relatively low at 61,600 cases and 1,039 deaths.
Under the vaccine swap deals, Australia will return equivalent numbers of Pfizer-BioNTech vaccines to Britain and Singapore later this year.
(Reporting by Renju Jose; editing by Jane Wardell)
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Buildings in the central business district of Sydney, Australia, on Friday, May 14, 2021. House prices have outstripped wage growth for years, leaving places like Sydney as one of the worlds most unaffordable housing markets.