NSW Premier Dominic Perrottet has flagged more new freedoms for the state next week, saying dealing with the COVID-19 pandemic is "one, two and three" on his to-do list.
"That is the sole focus of the government," Mr Perrottet told AAP.
"We need to get through this as well as we can. We're going to lead the nation out of this pandemic here in NSW, and there's so many things to do in that space."
Some 444 new local COVID-19 cases were diagnosed in the 24 hours to 8pm on Tuesday and another four deaths as the state rapidly approaches its next vaccination milestone.
Some 75.23 per cent of residents over 16 are fully vaccinated and 90.77 per cent have had at least one dose.
NSW could reach the 80 per cent fully vaccinated milestone by Sunday, just days into the reopening triggered on Monday after 70 per cent of eligible residents got both jabs.
That will set the stage for the next phase in the state's reopening to begin next Monday, a week earlier than expected.
"The success of our vaccination rate has been absolutely superb ... When we hit 80 per cent, we've always said it will be the Monday following," Mr Perrottet said.
The government's COVID-19 and economic recovery committee - formerly known as crisis cabinet - will discuss tweaking the reopening roadmap on Thursday.
Mr Perrottet could announce changes to regional travel rules and other restrictions on Friday.
This may include the further postponement of regional travel given the lower vaccination coverage in rural communities.
As things currently stand, the next phase of the roadmap paves the way for outdoor gatherings of up to 50 vaccinated people, 20 guests in a home, dancing at hospitality venues and drinking standing up at the pub.
Travel across NSW would be allowed, as would carpooling, weddings of any size if the venue is large enough, and community sport.
But the state continues to record hundreds of new cases a day, with more than 700 COVID-19 cases in hospital.
Some 150 people are intensive care, half of whom require ventilation.
Of the four people who died on Tuesday - all from west or south west Sydney - three people were in their 70s and one in their 60s.
Two were fully vaccinated but had underlying heath conditions.
Meanwhile, Customer Service Minister Victor Dominello says the Service NSW app's vaccination passport function could be rolled out statewide sooner than next Monday.
He said the regional pilots for the function are progressing well, while the app's security settings will be boosted - including the removal of dates of birth from vaccination passports.
