Dutton, one of the most senior ministers in the federal government, said that Australia was not in the same "mad panic" as other countries to inoculate the population against Covid-19, reports Xinhua news agency.
He compared Australia's situation to that in the US and the UK, where he said there are thousands of new cases every day.
"We haven't lived in that environment, (and) we don't want to," Dutton told Sky News Australia.
"There will be hiccups from time to time in terms of the rollout of the vaccine, but we'll work with the states, we'll work with general practitioners."
His comments came after Nine Entertainment newspapers reported on Sunday that the first phase of the vaccine rollout will not be completed until the end of May, almost two months later than the early April deadline previously set by the government.
As of Saturday evening, Australia's vaccination tally was at 841,885, according to Minister for Health Greg Hunt.
That figure includes a 44-year-old Melbourne man who was admitted to hospital recently for blood clots about two weeks after receiving the AstraZeneca vaccine.
"There is one case which has been under investigation with regards to potential side effects and clotting. That will be determined through the medical processes, but I want to thank our medical experts," Hunt told reporters on Sunday.
"We will continue following their advice as we have done through the pandemic."