New South Wales has reported a record 6,394 new coronavirus infections, up from 6,288 a day earlier.
Case numbers in Australia's most populous state have surged over the past two weeks.
Hospital admissions had lagged behind new infections but have now risen sharply.
Thousands of people were isolating at home after contracting the virus or coming into contact with someone who had.
Doctors and pharmacists in New South Wales have said they are running short of vaccine doses amid a rush for shots spurred by concern over the Omicron variant.
More than 70 per cent of cases in some Australian states are the Omicron variant of the coronavirus but New South Wales does not routinely carry out genome testing to identify the variant. State Health Minister Brad Hazzard indicated on Sunday that Omicron is widespread.
“We would expect that pretty well everybody in New South Wales at some point will get Omicron,” Mr Hazzard said. “If we’re all going to get Omicron, the best way to face it is when we have full vaccinations including our booster.”
Speaking in Sydney, Premier of New South Wales Dominic Perrottet urged residents who “do not feel unwell” or have not been advised by health authorities to have a PCR test, to not seek one.
“You are taking the spot in the queue from somebody who needs a test,” he said.
In total, 458 people are in hospital with Covid-19 in the state, including 52 in intensive care.
Victoria, the country's second most populous state, reported 1,608 new Covid-19 cases and two deaths on Sunday, with 374 people in hospitals, including 77 in intensive care.
More than 30,000 people in Victoria spent Christmas isolating at home, unable to celebrate with family or friends. Of those, about half were reported to be active cases who contracted the virus in the days leading up to Christmas.