From July 16 all inbound arrivals to Australia will have to declare their vaccination status.
A home quarantine pilot program will also proceed in South Australia for arrivals vaccinated against COVID-19.
That was an important development, Prime Minister Scott Morrison said following the 46th national cabinet meeting with state and territory first ministers.
"I think it's trialling out these new quarantine arrangements which will take significant pressure off [the states and territories], if it's successful," Mr Morrison said on Friday.
A new communication campaign will also be coming soon for the vaccination rollout, he said.
"This is the next phase of those communication campaigns and coincides neatly with the additional supply that is being brought forward to support the vaccination program," Mr Morrison said.
More than 900,000 Australians have received a COVID-19 vaccine since last Friday's national cabinet meeting, where the government opened the door for anyone over the age of 16 to opt into taking AstraZeneca rather than waiting for the preferred Pfizer doses to become available.
A total of 8,871,572 vaccines have been administered since the start of the rollout, to 32.2 per cent of the population in Australia aged 16 or older, with 10.5 per cent of the eligible population in Australia now fully vaccinated.
Australia's weekly supply of Pfizer vaccine doses is set to triple, in what the prime minister hailed as a shot in the arm for the nation's beleaguered rollout.
The federal government announced Pfizer supplies would rise to roughly 1 million per week from July 19 - up from between 300,000 and 350,000 currently.
The pharmaceutical company confirmed the total volume of Australia's order had not changed.
"Pfizer is committed to delivering 40 million doses of the Pfizer-BioNTech COVID-19 vaccine to Australia over 2021. The total number of 40 million doses we are contracted to deliver to Australia over 2021 has not changed. We continue to work closely with the government to support the ramp up of their rollout program," Pfizer said in a statement.
"While the details of our agreement with the government are confidential, we can confirm that deliveries to Australia remain on track, and we continue to update our weekly delivery schedule in line with the ramp up. We expect the remainder of the 40 million doses to be delivered by the end of 2021."
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Labor health spokesman Mark Butler seized on Pfizer's statement, claiming it showed there was "nothing new" in Mr Morrison's vaccine supply announcement.
"When the prime minister is not in hiding he pops his head up to mislead the Australian people," Mr Butler said.
"It's time the prime minister did his job and took responsibility for his bungled vaccine rollout - and fixed it."
Labor leader Anthony Albanese said despite "government spin", a significant increase in vaccine supply was not being seen in GP clinics.
"It's good that he's now acknowledging that it's shortage of supply that is the problem. It is shortage of supply that means that people who want to get vaccinated, who are ringing up GP clinics ... can't get access to the vaccine," Mr Albanese said.