Independent MP Rebekha Sharkie has asked Health Minister Greg Hunt to look into the cases of several South Australian pensioners who were out of pocket for pre-vaccine consultations.

"Some risk not getting vaccinated at all due to the cost - what can be done to address this issue?" she asked during Question Time on Thursday.

Mr Hunt, who has referred the complaints to the health department, said the vaccine program was based on three principles: free, voluntary and universally available.

"Vaccination providers cannot charge to administer the COVID-19 vaccine," he said, adding this included booking fees and the cost of the vaccine itself.

The national vaccination program has reached 408,000 doses, with 49,500 delivered in the past day - well up on the 30,000 given on the first day of the GP-led program on Monday.

"Our GPs have been magnificent," Mr Hunt said.

He noted all GP clinics enrolled in the program had now received at least some doses, except one - Taree on the NSW mid-north coast, which has been hit by severe flooding.

Deputy Chief Medical Officer Michael Kidd said another 3500 general practices would start administering vaccines to their local communities over the next four weeks.

"We will be ramping up very quickly over the next couple of weeks to distribute over 400,000 vaccines a week," he told the ABC.

"That will increase further as more of the batches come through from CSL."

There are still concerns over delays of vaccines on order from overseas.

Australia is still waiting on almost four million doses of AstraZeneca vaccines from Europe.

Professor Kidd still expects to receive the shipment, along with 20 million doses of the Pfizer vaccine, by the end of this year.

But he is much more relaxed now that AstraZeneca vaccines are being produced in Australia.

"With CSL production now happening on shore, we are no longer dependent on overseas supplies," he said.

"We still have contracts for additional doses of AstraZeneca vaccines from overseas, but we now have surety of supply with the CSL production."

Prime Minister Scott Morrison is also talking up the value of locally made vaccines.

"The decision to have a domestic manufacturing capability here has been the big game changer," he said.

"We would not have a vaccine program were it not for the wisdom of that decision."

Phase 1b of the program takes in everyone over the age of 70, along with Indigenous Australians over 55 and younger adults with a medical condition or disability.

Workers deemed critical or high risk can also apply.

Australian Associated Press