NSW added 1116 locally-acquired COVID-19 cases in the 24 hours to 8pm Tuesday.
Four deaths were also recorded: four women who were not vaccinated and had underlying health conditions, Ms Berejiklian said.
They were aged in their 50s, 60s, 70s and 80s.
There now are 917 people in hospital due to COVID-19, 150 people are in intensive care units and 66 on ventilators.
About 148,000 people across the state were vaccinated yesterday and there were more than 170,000 tests.
Premier Gladys Berejiklian said: "It's really assisting us in getting to that 70 per cent double-dose figure sooner than we had anticipated. So that's fantastic news."
She hinted that international travel could return for NSW residents after the state hits its target of 80 per cent fully vaccinated, a milestone, Ms Berejiklian says, is expected in November.
This morning Victoria reported 120 cases of COVID-19 - the highest daily tally recorded since August 2020.
Victorian Premier Daniel Andrews is expected to announce the state's roadmap out of lockdown today, which many are seeing as a concession returning to COVID-zero is unlikely.