The newspaper said the shipments to Australia were never at the expense of the UK's vaccine rollout, citing an anonymous British government official.
"The government has. not set, nor has any plans to set any new targets for completing first doses", the prime minister said in a Facebook post.
"That's definitely the aim, that's the goal as we've said, to try and have all Australians have a dose by the end of the year".
Given Australia's heavy reliance on AstraZeneca's COVID-19 vaccine, the government has scrambled to secure millions of additional Pfizer doses from overseas to ensure the entire population can be vaccinated safely.
But that deadline was later retracted.
They include Health Minister Olivier Véran, a neurologist aged 41, who was given the AstraZeneca vaccine live on television on February 8.
Mr Hunt on Sunday said Global Positioning System have "flocked" to participate in the vaccine program in the coming week.
"The UK, for example, is also dealing with the fact they're not going to be giving AstraZeneca to young people but they've been able to substitute the Moderna vaccine, a highly effective state of the art MRNA vaccine, and will soon be subsititing the Johnson and Johnson vaccine as well".
"On indemnity, I want to make something very, very clear", he told reporters in Melbourne.
"The details of any commercial vaccine supply agreements between national governments and AstraZeneca are commercially sensitive and a matter for those two parties". "I am saying this on behalf of the government but also on behalf of our legal advice, no doctor need worry".
More than 996,000 coronavirus vaccine doses have now been administered across Australia.
"Based on previous studies which combine different vaccine types, a combination of the AZ and Pfizer vaccines is likely to be safe but it's important that this is tested in the context of a clinical vaccine trial", said Helen Fletcher, professor of Immunology at the London School of Hygiene and Tropical Medicine.
"They will offer you what they believe to be of medical benefit to you and explain any risks and benefits of having or not having the treatment".
Head to www.health.gov.au for information on this.
"We are now in a very hard situation", Mr Butler told ABC's Insider program on Sunday.
"A range of experts in Australia were saying that best practice was to have more than four deals, five, six deals, the United Kingdom has seven deals on the table, to ensure redundancy in our system, to ensure there was a backup when something like the AstraZeneca advice arose", Mr Butler said.
"They should have listened to the expert advice that was given to the government, and indeed to all governments, about not placing all our eggs in one basket".