Health secretary Brendan Murphy raised doubts about the October target last week when facing a Senate inquiry.

The first AstraZeneca doses that are being produced in Australia are expected to be available the week after next, and Prof Murphy said he is now working with CSL to increase their production.

He said if production of the vaccine remains as it is, there may be some Australians who have to wait for a second jab in the weeks after October.

"If we get extra AstraZeneca production from CSL, I imagine all Australians will potentially have received it by the end of October," Prof Murphy told reporters at a Sydney clinic where Prime Minister Scott Morrison and Chief Medical Officer Paul Kelly received their second Pfizer jab on Sunday.

Mr Morrison said the critical factor in controlling the pace of the vaccination program is the supply and the production of vaccines.

"That is the critical swing factor," he told reporters.

It is estimated that Australia is 3.1 million doses short of the AstraZeneca vaccine in the initial phases of the rollout.

Mr Morrison said Health Minister Greg Hunt and Prof Murphy would be providing regular updates on the vaccine rollout from Monday week.

The government is providing a further $1.1 billion to extend the national COVID-19 health response until the end of the year.

This comes on top of the $22 billion already spent to date, including more than $6 billion to support the virus vaccine rollout.

"Australia's suppression strategy has been extremely successful to date, particularly when compared with the devastation caused by the virus in many places overseas," the prime minister said.

"Australia's remarkable performance in saving lives is evident - we have the second lowest case rate and third lowest mortality rate amongst countries in the OECD."

But Opposition Leader Anthony Albanese said Australia is not in a better position than the rest of the world with regard to the vaccine rollout.

He said the government had said four million people would have got their first jab by the end of this month but with just over two weeks to go, only about 150,000 people have been vaccinated.

"We are way way short," he told Sky News' Sunday Agenda program.

"We had Scott Morrison in his usual way say that black is white and suggest that he hadn't really meant that everyone would be vaccinated by October when they have said they would on multiple occasions."

The government is also ramping up its campaign against misinformation on the COVID-19 vaccines with a new website - "Is it true" - on www.health.gov.au/covid19-vaccines.

"This new function will provide trusted, credible information on COVID-19 vaccines for everyone in Australia," Mr Morrison said.

"It will sort the fact from the fiction."

Meanwhile, NSW's 56-day run of no locally acquired coronavirus cases has come to an abrupt halt after a person who works in two quarantine hotels contracted the disease.

NSW Health said the source of the Sydney worker's infection remains unclear, and the testing of their close contacts is underway.

Mr Morrison confirmed that the person had been vaccinated.

Prof Kelly explained there is a time lag between getting the vaccine and the protection kicking in.

"Once you are vaccinated you still have to try and observe as you should the Covid-safe behaviours," Mr Morrison added.

Australian Associated Press