Scott Morrison has taken to Facebook to reassure Australians the government's COVID-19 vaccination program is safe and rolling out in a timeframe comparable to other countries.

The prime minister launched the video message as the government faced a swathe of criticism over the pace of the rollout and concerns about the safety of the country's mainstay AstraZeneca vaccine.

The government abandoned any target time to complete the vaccination program after medical authorities recommended people under 50 get the Pfizer vaccine instead of AstraZeneca because of rare blood clotting concerns.

Mr Morrison said targets were not possible as COVID "writes its own rules".

"You don't get to set the agenda," he said.

"You have to be able to respond quickly to when things change and we've had to deal with a lot of changes.

"Rather than set targets that can get knocked about by every to and fro of international supply chains and other disruptions that can occur, we are just getting on with it."

The government has also reportedly confirmed the Johnson & Johnson single-dose Janssen vaccine jab will not be part of Australia's vaccination program "at this time".

This appears to be because the vaccine is similar to the AstraZeneca one.

"The Janssen vaccine is an adenovirus vaccine, the same type of vaccine as the AstraZeneca vaccine," the office of Health Minister Greg said in a statement cited by the ABC and other media.

"The government does not intend to purchase any further adenovirus vaccines at this time."

The Health Department is now publishing daily vaccination data updates online.

Mr Morrison said Australia's current rate of 1.2 million vaccinations to date was comparable to other major countries.

"You will be able to keep track of that program and how we compare to countries overseas," he said in the Facebook post on Monday.

Government figures show Australia's rollout, compared to 12 other nations, is running behind the UK, US, Singapore, Belgium, Italy and Germany.

Once frontline health workers and other priority groups were vaccinated, Mr Morrison said there would be an "opportunity later in the year, I think, to do things at a more ramped up scale".

NSW Premier Gladys Berejiklian said she had a sense of urgency, as the trajectory of the virus itself could change at any time.

"There will come a point in time when we could be left behind if we don't accelerate what the current plans might be," she said.

Labor health spokesman Mark Butler said it was not possible to have a plan without a target.

"It is simply not a plan," he said.

"The health of Australians depends upon it and strengthening our economic recovery rests very squarely on the effectiveness on the vaccine rollout."

The government says 40 million doses of the imported Pfizer vaccine should be available by the end of the year, on top of the local supply of the AstraZeneca version.