NSW has administered nearly a million COVID-19 jabs, with the AstraZeneca vaccine now available across the state at GP surgeries to everyone aged 50 and older.

Gladys Berejiklian is pleased with the uptake of the COVID-19 vaccine with almost a million people in NSW receiving a jab so far.

The premier outlined her ambition for international borders to open "sooner than the middle of next year" based on her desire for most of the state's six million adults to be vaccinated as soon as possible.

"NSW is edging towards a million jabs being administered," Ms Berejiklian said on Monday.

"If we get the majority of our population vaccinated, then we can think of opening our international borders."

She was speaking at Sydney's Olympic Park mass vaccination hub on the first day that everyone 50 and older is able to book in to get an AstraZeneca jab from their GP.

More than 16,000 people aged 40 to 49 have been contacted to make an appointment at Sydney Olympic Park after registering their interest to receive the Pfizer vaccine.

The premier said there was "good strong demand" in the community to be vaccinated, with some centres "providing a few jabs every minute".

The total number of doses given in NSW to 8pm Sunday night stood at 926,242, with more than 100 sites administering the vaccine.

NSW Health is pushing to administer 10 million jabs to vaccinate every willing adult.

"The quicker the vaccine is rolled out the quicker we will be able to ease restrictions and resume a normal existence during COVID," Ms Berejiklian said.

She urged people to get vaccinated while acknowledging some anxiety among people over 50 about getting the AstraZeneca vaccine, which in rare cases has been linked to blood clots.

"Both vaccines are effective ... no vaccine is 100 per cent ... but we're aimed at preventing people dying."

"I appreciate some people may be concerned ... I would encourage people who have access to a safe vaccine to have that vaccine," she said.

NSW Health Minister Brad Hazzard also urged people to get whatever vaccine is available to them.

"Straight outside our borders there are hundreds of thousands of people dying ... and that could happen ... have the vaccine" he said.

"It's up to each and every one of us to step forward and have the vaccine."

NSW recorded no new locally acquired cases of COVID-19 in the 24 hours to 8pm on Sunday, with the missing link from the recent Sydney outbreak still unknown.

Meanwhile, COVID restrictions have eased across Greater Sydney with no more limits on visitors to homes, dancing and singing.

Masks are no longer compulsory - although they remain recommended - on public transport.