Confusion over the rollout has reigned after Prime Minister Scott Morrison encouraged people under 40 to talk to their doctor if they wanted the AstraZeneca vaccine in a press conference late on Monday night.

Federal and state politicians have traded barbs after Mr Morrison's "captain's call" caused a swathe of mixed messaging about the already troubled rollout.

Other state and territory leaders did not back the Prime Minister's call, particularly Queensland Premier Annastacia Palaszczuk who came out strongly against the Prime Minister's comments and urged young Australians to not receive the vaccine.

This prompted the federal Finance Minister Simon Birmingham to say Ms Palaszczuk was spreading "extremist" claims.

Chief Minister Andrew Barr was asked about Mr Birmingham's comments on Thursday and said recent commentary was unhelpful, while urging for clarity on the vaccine rollout.

"I don't think it's been particularly edifying for the country to witness what's happened over the last several days," he said.

"It's undermined confidence in the vaccine program and it's just generally been unhelpful.

"I think right now what the country wants from national cabinet, from our political leaders is clear and consistent messaging and engagement around an accelerated vaccine rollout."

The Chief Minister's comments come after he accused the Prime Minister of making a "captain's call" when he encouraged people under-60 to talk to their doctor if they wanted to get an AstraZeneca jab.

Mr Barr said on Wednesday that he was surprised by the Prime Minister's Monday night comments and that it was not discussed at Monday's national cabinet meeting.

The official health advice from the government's vaccine panel, ATAGI, is that the AstraZeneca jab is not recommended for people under 60 due to an extremely rare blood clotting disorder.

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But under-60s can access the vaccine if they give informed consent, Mr Morrison also announced legal protection would be offered to doctors who give the vaccine to younger people who consent. Pfizer is the preferred vaccine for younger people.

Mr Barr said a lack of Pfizer vaccine was the reason for the troubles in the rollout.

"That's the fundamental issue. We're going to get those supplies, we hope, in the months ahead," he said.

"But in the interim, I don't think we're doing the nation a service by this sort of political debate that is occurring.

"My message to everyone is let's just lower the temperature on this.

"I don't think this is something we need to score political points on, frankly."

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