They were four women and two men, with one in their forties, one in their sixties, two in their seventies and two in their eighties.
Half of them were unvaccinated and half had had one dose.
One of the men in his 70s who died acquired his infection overseas.
There are currently 1219 COVID-19 patients in the state's hospitals, including 233 in intensive care, with 123 of them on ventilators.
Of the 233 people in intensive care, 173 are not vaccinated, 55 have had one dose of a vaccine, and five are fully vaccinated.
NSW records 1,331 locally acquired COVID cases
Dr McAnulty said fragments of the virus had also been detected in the wastewater systems servicing Byron Bay, Wardell, Eden, Balranald and Griffith.
The majority of the state's COVID-19 infections continue to come out of western and south-western Sydney, with NSW Health highlighting Merrylands, Auburn, Guilford, Liverpool, Bankstown, Greenacre and Punchbowl as key areas of concern on Saturday morning.
"But no matter where you live in New South Wales, it's important you get the message that if you get any symptoms, you come forward for testing right away," Dr McAnulty said.
Of the 1331 new cases, 169 were in regional NSW, including 75 in the Illawara, 30 in Hunter New England, 29 on the Central Coast, 17 in western NSW, eight in southern NSW, six in far western NSW and four in the Murrumbidgee.
Health authorities on Saturday launched a vaccination blitz of 18 Sydney social housing blocks.
Mobile teams including social workers, interpreters and cultural support workers are part of the program at Redfern and Waterloo.
"Our teams will move from building to building, ensuring every resident has access to information on COVID-19 and vaccinations," district health chief Teresa Anderson said.
Saturday's data showed 50.6 per cent of the eligible population aged more than 16 had been fully vaccinated as of Friday.
Across the state, 81.2 per cent have received a first jab.
"This is fantastic news. Thank you so much for coming forward to get vaccinated and help us get out of this epidemic," Dr McAnulty said.
In total, there have been almost 3.2 million vaccination doses administered in NSW.
Additional reporting: AAP