Premier Gladys Berejiklian has urged NSW residents not to let visitors from coronavirus hot spots in Melbourne into their homes.
"You have the right to say no," she said at a news conference on Tuesday.
NSW recorded five new cases in the 24 hours up until 8pm on Monday, all returned travellers, who are in hotel quarantine.
In contrast, Victoria recorded 64 new cases, the fourteenth consecutive day of double-digit increases in the state.
Ms Berejiklian said tomorrow (July 1) was "a big day for us" in NSW, with a further easing of restrictions affecting many areas of life.
"But, things can change very quickly in terms of community transmission," she said.
"I have noticed in and around my movements people are starting to relax a little too much for my liking.
"Don't relax!. Assume everyone in and around you has the disease."
A total of 12,950 tests were notified in NSW in the last 24-hour reporting period, compared with 11,833 tests in the previous 24 hours.
NSW has carried out more than 855,000 COVID-19 tests.
"Due to the concerted effort of all residents, NSW has successfully suppressed COVID-19 to very low levels," said Dr Jeremy McAnulty, from NSW Health.
"However, Victoria is seeing increased COVID-19 activity within some areas of Melbourne.
These areas are being closely monitored and interventions to prevent further transmissions from these areas are being implemented by the Victorian Government.
"Non-essential travel between Melbourne and NSW is strongly discouraged.
"In addition, restrictions on workers and visitors who have been in Melbourne in the previous 14 days to high risk settings have been implemented.
"Further restrictions may be implemented as the situation evolves. NSW Health will continue to closely monitor the situation and provide regular updates to keep the public informed."
