The entire state is currently locked down and police are cracking down on compliance measures as authorities battle to contain the spread of the virulent Delta strain.
The six deaths recorded in the 24 hours to 8pm on Saturday included three people in their 80s and three in their 70s. None were fully vaccinated.
The death toll for the current outbreak now sits at 89.
There are now more than 810 COVID-19 patients in NSW in hospital, with 126 in intensive care and 54 ventilated.
Of those 126 in intensive care, only one was fully vaccinated.
NSW Premier Gladys Berejiklian says the state could reach 70 per cent single-dose vaccination coverage within days, having already surpassed 65 per cent.
"At this stage, the double dose at 70 per cent will give us more freedoms. We expect that to land somewhere during October," Ms Berejiklian said.
"But the next big target I want us to achieve is that 70 per cent single-dose vaccination because then we will have confidence as to when we are going to (reach) that double dose."
It comes as paramedics in NSW are becoming increasingly stretched by the state's accumulation of COVID-19 infections, with demand equivalent to the "busiest New Year's Eve".
At least two western Sydney hospitals - Westmead and Blacktown - have called "code yellows" this week as their caseload climbs.
NSW Ambulance Commissioner Dominic Morgan on Saturday said there had been so many calls for ambulances in the previous three days it was the equivalent demand on paramedics as the "busiest New Year's Eve".
On Friday alone, Mr Morgan said 450 patients required paramedic assistance for suspected or actual COVID-19.