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"This is not over. There's a long journey to go," he said on Monday.
The Australian state reported 265 new locally acquired cases and five deaths - four women and one man - in the 24 hours to 8pm on Sunday as a swathe of restrictions eased for fully vaccinated adults.
One of the deaths involved a woman in her 30s from Cessnock who died at John Hunter Hospital. She was not vaccinated and had underlying health conditions.
After announcing last week the scrapping of hotel quarantine for fully vaccinated international arrivals from next month, the New South Wales' premier said the state was "leading the nation out of the pandemic".
"We are well positioned to help all Australians around the world come home and we want to get tourism back. We need to open up as quickly as possible and as safely as possible."
However, Mr Perrottet acknowledged case numbers and hospitalisations were expected to increase again in the coming weeks, with targeted restrictions reintroduced if necessary.
"As mobility increases across the state, case numbers will increase. That will be a challenge for our state but our health system is very strong."
More than 80% of people over 16 are now fully vaccinated, which on Monday triggered a second-stage easing of restrictions.
At least one dose of the vaccine has been given to 92% of adults.
The premier, who revealed he and his wife Helen are expecting their seventh child, was one of thousands of parents who took their children to school on Monday for the first time in more than four months.
Home schooling is over for more than 148,000 students in kindergarten, year one and 12. Other years will return next week.
Mr Perrottet announced another $A50 million ($NZ62 million) to extend the now $383 million school tutoring programme into next year.
Education Minister Sarah Mitchell said the programme employed 7500 tutors to help children.
About 90% of school staff were vaccinated, Ms Mitchell said, but students were advised to wear masks indoors until restrictions eased further.
Mr Perrottet said he had reached out to neighbouring Victorian Premier Daniel Andrews about co-operating over border arrangements as both states emerged from lockdown.
"Their case numbers are still high but it's pleasing to see they are opening up," he said.
1903 cases in Victoria, border to open
Victoria on Monday reported 1903 new cases, up from 1838 a day earlier. State authorities disclosed on Sunday that Melbourne, the state capital, will exit its lockdown on Friday as the state looks poised to reach its 70% vaccination target within days.
Melbourne's 5 million residents have been enduring an extended lockdown since August 5, the sixth in the pandemic, and have already spent around nine months under strict stay-home restrictions since March 2020 - the longest in the world, according to Australian media.
From Wednesday, fully vaccinated people travelling from NSW red zones can go to Victoria without quarantining after a negative Covid-19 test but must isolate and get tested again within 72 hours of their arrival.
People entering NSW from Victoria are still required to complete an entry declaration form and quarantine at home for 14 days.
The second stage of the NSW roadmap out of lockdown means outdoor gatherings of up to 50 fully vaccinated people are now permitted and up to 20 visitors are allowed in a home, provided everyone over 16 is vaccinated.
People can stand up while drinking and even dance in most hospitality venues, but not yet in nightclubs, which are allowed to reopen so long as people sit down while they drink.
There is no limit on weddings and funerals and the five-person cap at hairdressers and beauticians is also gone.
Vaccinated office workers are no longer required to wear masks at work, but masks are still required in other indoor areas such as on public transport or in a shop.
Meanwhile, a tribute to frontline workers and those who have been vaccinated will be projected onto the sails of the Sydney Opera House on Monday night.
There are 606 Covid-19 cases in NSW hospitals, with 132 people in intensive care and 71 on ventilators.
There have been 475 Covid-19 related deaths in NSW since June 16, and 531 since the start of the pandemic.
- additional reporting by Reuters