"While we would like to see these doses completed before the end of the year, it is not possible to set such targets given the many uncertainties involved."
His decision to throw out the vaccine timetable has thrown the rollout into chaos but Jane Halton from the National COVID-19 Commission is calling for calm.
"The trick now is for people just to calm down a little bit and get back to basics," she told Nine on Monday.
"We need to vaccinate the nation, we need to have the vaccines to do that, we're going to get Pfizer at the end of this year and there will be 40 million doses in total of Pfizer."
Epidemiologist Mary-Louise McLaws says unless national vaccination rates ramp up to between 100,000 and 120,000 per day, it will take two years for Australians to be fully vaccinated.
The latest daily tally was 27,209.
The McKell Institute has found vaccine delays will increase the chance of lockdowns and hurt the economy, warning to cost could be more than $1.4 billion.
Earlier on Sunday, senior minister Dan Tehan told Sky News' Sunday Agenda program the government's aim was to have all Australians injected with at least one dose of the vaccine by the end of the year.
But that deadline was later retracted.
"We will just get on with the job of working together to produce, distribute and administer the vaccines as safely and efficiently as possible," Mr Morrison said.
The rollout was thrown into disarray last week after health authorities recommended AstraZeneca vaccines should only be given to Australians aged over 50, following concerns about blood clotting.
GPs 'flocking' to vaccine program
Health Minister Greg Minister has insisted GPs have not been put off participating in the rollout of COVID-19 vaccine program because of the AstraZenaca advice.
And for any doctors who may be concerned about being sued if it was administered to a younger person, he says vaccine indemnity agreements are already in place.
Mr Hunt on Sunday said GPs have "flocked" to participate in the vaccine program in the coming week.
But there are also reports that doctors are concerned that if they give an AstraZeneca jab to a younger person they could be sued if there are resulting problems.
Mr Hunt said while Pfizer is preferred for those under 50, AstraZeneca is available, subject to the medical discussion between a doctor and their patient.
"On indemnity, I want to make something very, very clear," he told reporters in Melbourne.
"Australia already has vaccine indemnity agreements in place. I am saying this on behalf of the government but also on behalf of our legal advice, no doctor need worry."
Australian Medical Association President Omar Khorshid said it is critical for Australia's future that public confidence in the vaccine program is maintained.
"Your GP will give you the best advice about any medicine or vaccine," he said.
"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. "
Labor's health spokesman Mark Butler said the government should have secured more vaccine deals to ensure there was a backup plan when something like the AstraZeneca situation arose.
"We are now in a very difficult situation," Mr Butler told ABC's Insider program on Sunday.
"Australia was already way behind schedule in the vaccine rollout, not in the top-100 nations in the world and a bad situation has been made far worse by these unforeseen events around the AstraZeneca vaccine."
But Mr Hunt said the government had followed the advice of health experts.
"There is no existing advice they have which has not been followed," he said.