The case numbers are a slight increase on the already record case numbers reported on Christmas Day.
Queensland has recorded 714 new cases, another daily record for the state, with seven people in hospital and none in intensive care.
Victoria reported a slight decrease in daily case numbers, with 1,608 new Covid-19 infections, including 374 in hospital.
It comes as thousands of Australians experienced a lonely festive season in isolation due to either contracting Covid-19 or coming into contact with a case.
The country is battling its biggest, most widespread outbreak, with the Omicron variant in every state and territory.
On Saturday, NSW reported a record 6,288 cases. Queensland similarly had a record 765 new infections, 151 of them of the Omicron variant, and in Victoria 2,108 people tested positive for the virus.
Also on Saturday, South Australia recorded 634 new cases, Tasmania had 33 cases, while the Northern Territory reported 19 cases, 10 of which were interstate arrivals.
Western Australia recorded two new local Covid-19 infections on Saturday, both linked to a French backpacker who arrived in the state from Queensland.
Mask wearing is compulsory in most states and territories, as leaders try to limit the spread of the highly infectious variant over the festive season.
Meanwhile, wait times for testing and results have blown out in several states.
As infections continue to rise, the federal government announced the wait for booster shots will be reduced twice in January.
Then from 31 January, people can get boosters after three months.
About 7.5 million Australians will be eligible for their booster shot come 4 January. This will jump to 16 million at the end of the month.
The federal health minister, Greg Hunt, praised Australians who have rolled up their sleeves for their third dose.
Some 123,500 shots were given on Christmas Eve, 94,072 of them boosters.
The prime minister, Scott Morrison, and the opposition leader, Anthony Albanese, used their Christmas messages to thank Australians for standing together and supporting each other during the pandemic.
Albanese said Australians deserved to have a happy Christmas after a challenging two years.
