NSW Premier Dominic Perrottet says unvaccinated people will not be granted freedoms any earlier than December 15 despite thousands rallying against vaccination requirements.

"All of these measures are not tailored for rules for the sake of the government, they are tailored to keep people safe and that's what we're focused on," Mr Perrottet said in Sydney on Sunday, the day after unmasked protesters descended on the city.

NSW recorded 176 new local COVID-19 cases and two deaths in the 24 hours to 8pm on Saturday.

An unvaccinated women in her 40s died at Sydney's Royal Prince Alfred Hospital and a fully-vaccinated man in his 80s died at Liverpool Hospital. Both had underlying health conditions.

The state is inching closer to the 95 per cent mark for first-dose vaccinations, with 94.4 per cent of residents over 16 years stepping forward for at least one jab. Some 91.8 per cent are fully vaccinated.

NSW Health's Dr Jeremy McAnulty said there had been multiple cases in schools across the state.

"We are urging parents to remain really vigilant to help protect the rest of the school community," he said on Sunday.

"Symptoms in children can be quite mild and not obvious so if they get any symptoms at all please take your children to a testing clinic."

Two Sydney schools and one in Newcastle remain closed due to COVID outbreaks.

Of the 12- to 15-year age group, 75.3 per cent are fully vaccinated and 81 per cent have received at least one vaccine.

The new cases in the 24 hours to 8pm on Saturday were diagnosed from 55,330 tests.

Some 192 people are hospitalised with the virus and 32 are in intensive care, 15 of whom required ventilation.

At least 104 of Sunday's cases were in Sydney, while Hunter New England was the regional health district with most new cases, recording 32.