Labor has thrown its support behind establishing stadium-style coronavirus vaccination hubs to speed up the national rollout.
The federal government has played down the need for mass vaccination sites, insisting its growing network of general practice clinics has the program under control.
Prime Minister Scott Morrison says GP clinics are currently the best option as the early stages of the rollout are focused on vulnerable Australians.
"Their GP knows their medical history, their GP has built up confidence with them over a long period of time," he told reporters in Canberra on Tuesday.
"They can talk to them about any questions or issues they might have about the vaccination."
Mr Morrison initially said four million people would be vaccinated by the end of March, but as of Monday close to 855,000 had been inoculated.
The prime minister has put the blame on supply blockages, with three million doses of the coronavirus vaccine never arriving from overseas.
Opposition health spokesman Mark Butler said the current strategy was not working and it was time for new ideas.
"These large vaccination centres of the type that state governments would be able to operate fairly straightforwardly are the way in which other countries are racing ahead of Australia in their vaccine rollout," he told ABC radio.
Mr Butler also wants pharmacists brought into the rollout sooner after chemists warned they had been delayed by a month and would not start administering coronavirus jabs until June.
He said it was unfair to force general practices to go it alone.
NSW Premier Gladys Berejiklian does not support the idea of mass vaccination hubs as she is concerned rural and regional communities will be ignored.
Health policy expert Bill Bowtell said the slow vaccine rollout was creating serious problems.
The adjunct professor said Australia had inoculated just 2.34 in every 100 people.
"We're somewhere about 90th on the world league tables - sandwiched between Bolivia and Albania," he told Melbourne radio 3AW.
"However you want to spin it, we are not doing very well."
Professor Bowtell said there were not only serious problems with both vaccine supplies and distribution, but the virus was mutating faster than Australia was vaccinating its population.
"It's a very serious situation," he said.
The United Kingdom has transformed churches and warehouses into vaccination hubs and the United States has used sporting stadiums.
Acting Chief Medical Officer Michael Kidd said federal health authorities were not ruling out the idea of mass vaccination sites.
"Each state and territory is looking at what is the best way to meet the needs of their local population and to get the vaccine out to the people of Australia."
Mr Morrison is due to meet with his state and territory counterparts on Friday.
He will push for more transparency and frequency on vaccination data.
Australian Associated Press