In a bid to encourage broader vaccination, the federal government also announced a no fault indemnity scheme for GPs who administer COVID-19 vaccines.

The scheme would enable, for example, a person under-60 who is happy to get the AstraZeneca vaccine - which is currently only recommended for over-60s - to do so if their doctor considers it is the best option.

Crown Medical Figtree practice manager Mary Shalala said demand for the AstraZeneca jab had been high since the practice joined the rollout in late March.

"When we started the demand was crazy, and it has remained constant since then," she said.

"There was a slight drop where people were being extra cautious due to reported side effects, but we still ran clinics every day.

"With the breakout and since the Prime Minister's announcement, the phones have been extremely busy.

"Already (by 11am on Tuesday) we have had our clinics pre-booked for the week."

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Ms Shalala said at the practice - which has over 10,000 patients on its books - a doctor and nurse were allocated to administer COVID vaccines each day.

"People get to see the doctor first and can ask questions before signing the consent form and getting the vaccine administered by the nurse," she said.

"Now that the AstraZeneca vaccine is available to all Australians over 18, we've had people 30 years and over calling to book in today.

"We will allow extra time for those under 60 who want the vaccine to talk to the doctor and make them aware of the risks and benefits."

Ms Shalala said in her practice at Figtree Grove the rollout had been smooth; they'd been able to keep up with demand and had no issues with supply.

"We're very fortunate that we've had no issues, and are receiving our 400 doses each week on time," she said.

Patients were now getting their second doses of the AstraZeneca vaccine at the centre.

"All our patients have waited the 12 weeks - there is some talk they can get their second dose sooner and certainly many would like to do that as they don't want to wait any longer than necessary," she said.

Ms Shalala said while running vaccine clinics meant a lot more work in an already busy practice, it was an easy decision to join the rollout.

"Because of the size of the practice, our doctors felt an obligation to do their part to give our patients a sense of security in such uncertain times," she said.

"We have also been flexible, we have an open-door policy allowing new patients to come to the practice for the vaccine."

At Tuesday's media conference NSW Premier Gladys Berejiklian said more GPs were needed to come on board with the vaccine rollout. The Commonwealth government is overseeing the rollout at GPs nationally.

"GPs want more jabs, they want more doses and they wants access to Pfizer," she said, adding that work was underway to provide that access.

NSW chief health officer Dr Kerry Chant urged those who became eligible for any vaccine to take advantage of the opportunity.

"We are trying to vaccinate the most vulnerable in our community," she said.

"Vaccines are very effective in stopping hospitalisation and death .. they do also have an impact on transmission."

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