CANBERRA -- Australia's coronavirus vaccine timetable remains uncertain, Secretary of the Department of Health Brendan Murphy has said.

Murphy recently told a parliamentary inquiry into Australia's response to the COVID-19 pandemic that he could not set a deadline for the completion of Australia's troubled vaccine rollout.

"At the moment we are not in a position to give an updated time on when vaccinations will be completed, but all first ministers want it completed as soon as possible," he said.

"There are still a number of uncertainties, even with a re-calibrated plan."

Murphy said that the government was hopeful of completing phases 1A and 1B of the program, which is focused on frontline health workers and aged and disability care, by May but conceded there was more work to be done for disability care residents.

As of Tuesday there had been 1.65 million vaccines administered in Australia.

The government has promised that the rollout of vaccines is ramping up but Omar Khorshid, the head of the Australian Medical Association, said vaccine skepticism had supplanted supply issues as the hurdle for the program.

"Our problem in the past was a lack of vaccines, but just in the last week or so, we've got a new problem and that is Australians have lost confidence in the vaccines," he told Nine Entertainment newspapers.

"A real challenge for our governments, for our medical profession, is to actually get Australians to go into their GP, roll up their sleeve and get their vaccine."

As of Tuesday afternoon, there had been 29,559 confirmed cases of COVID-19 in Australia, and the numbers of locally and overseas acquired cases in the last 24 hours were zero and 15 respectively, according to the latest figures updated on Tuesday evening from the Department of Health.