818 new cases of transmission were recorded in the 24 hours to 8pm Sunday, with three people in their 80s dying in that period. NSW Premier Gladys Berejiklian said all had underlying conditions.
She urged people to turn away from case numbers in favour of watching vaccination rates.
"Once we get to 80 per cent double dose, essentially we will have normalised COVID the way we treat other conditions," she said.
She said there would be "more to say" about a return to schools later this week given how close the 6 million vaccinations target had come.
Ms Berejiklian said 738,000 people were vaccinated in NSW during the past week.
"We're up to 5.9 million jabs in NSW," Ms Berejiklian said. "I'm so pleased everybody has really heard the call."
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Federal Health Minister Greg Hunt told reporters in Canberra on Monday that vaccination rates in recent weeks had begun to match records around the world.
More than 139,000 people were vaccinated nationally on Sunday.
"All of those numbers are progressively increasing," he said.
"Supply is strong, distribution is strong and the uptake is incredible."
Monday delivered tighter NSW lockdown rules, including for the Hunter. Masks are now mandatory outdoors in the region until August 28, the mooted expiry of the statewide lockdown.
Curfews have now come into force across Sydney's 12 local government areas of concern, with that city's lockdown not due to expire until the end of September at the earliest.
Across the border Victoria recorded 71 new cases of COVID-19 in the 24 hours to midnight yesterday.