Health authorities have said it is "likely" the vaccine is linked to a 44-year-old Melbourne man being hospitalised with blood clots, almost a fortnight after he received his injection.
But Health Minister Greg Hunt said Australia's medicine regulator, the Therapeutic Goods Administration (TGA), and an expert advisory group on vaccines maintain the AstraZeneca jab is safe - but are continuing to investigate the incident.
He said authorities had put the vaccine through rigorous testing before allowing its use across the country.
"If anybody is susceptible [to blood clots], they ought to consult their general practitioner," Hunt told reporters on Sunday afternoon.
"This very considered medical process reaffirms exactly why … Australia sought to have a full, thorough and absolute safety process in assessing the vaccines.
"The course of events reaffirms that this is the right approach."
The federal government has been widely criticised for delays in the vaccination programme, which so far uses the Pfizer and AstraZeneca vaccines, with the accusation it has woefully under-delivered with regards to the number of Australians vaccinated so far.
Labor continues to cite a commitment from the Commonwealth that 4 million doses would be delivered to Australians by April.
Hunt said the vaccination rate was steadily increasing by the day, with almost 842,000 doses being administered since the programme started more than a month ago.
A record number of daily vaccinations, more than 79,000, were recorded on Thursday.
Locally manufactured doses of the AstraZeneca vaccine, produced in Melbourne, were also adding to stockpiles across the country.
"It's supply that determines the rollout," Hunt said.
"As the supply has increased, with sovereign vaccine manufacturing, so has the rollout."
The minister avoided putting a timeframe on when phase 1A and 1B of the vaccination programme, focusing on frontline health workers and older Australians, would be completed.
"That's simply not good enough," Shadow Health Minister Mark Butler said in Adelaide.
"Australians deserve to know when they will get their vaccine and until we've completed these early phases, the other phases will simply not be able to commence."
Butler argued the federal government's failures were most clear in the slow pace of vaccinating aged care residents and workers, a federal responsibility.
"The states have made very good progress in vaccinating their own frontline health workers and others within their jurisdiction, but the Commonwealth has made a mess of its responsibilities to vaccinate the most vulnerable people in our community, residents of aged care facilities, and the hundreds of thousands of people who work so hard caring for them," he said.
Prime Minister Scott Morrison has tried to knock back criticism of the vaccination programme by saying Australia is in a vastly different situation than other countries, such as the United States and United Kingdom, where daily Covid-19 case numbers remain in the thousands.
The US Centres for Disease Control and Prevention said more than 157 million doses of coronavirus vaccines had been administered across the United States.