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Sydney is one step closer to freedom with Gladys Berejiklian's target of six million Covid vaccines hit today - even as 753 new cases were recorded.

Of the locally acquired cases, 134 are linked to a known cluster, 108 are household contacts and 26 are close contacts.

The source of infection for 619 cases is under investigation, and no deaths were recorded in the 24 hours to 8pm on Monday.   

On Tuesday morning, she said 60 per cent of the state's population has had at least one jab and 32 per cent have had one - 48,761 vaccines were administered on Monday.

The NSW premier has long promised the target of six million jabs would trigger 'greater freedoms', at least for the 31 per cent in the state fully vaccinated.  

Those are likely to be extremely limited with NSW recording more than 800 cases a day, the vast majority in western Sydney.

'I'm so pleased and grateful New South Wales has had 6 million jabs,' Ms Berejiklian told reporters on Tuesday morning.

'We have hit the milestone and I look forward to making the announcement on Thursday or Friday this week as to what fully vaccinated people will be able to do from the month of September because of the target we have set.'    

Premier Gladys Berejiklian promised on Monday that fully vaccinated NSW residents that they will have 'at least one' freedom restored. Pictured: a woman in exercising in Sydney

Seventy-three cases were in isolation throughout their infectious period and 22 were in isolation for part of their infectious period.   

There are 608 Covid-19 cases admitted to hospital, with 107 people in intensive care, 34 of whom require ventilation. 

Thirty-six new cases were recorded in far west NSW, including 23 in Dubbo, 14 in Wilcannia and five in Parkes. 

The 12 local councils of concern in the city's west woke up to their second day of even harsher restrictions on Tuesday, including a curfew and one-hour exercise limit. 

Areas of concern include Burwood, Fairfield, Canterbury and Bankstown, but Ms Berejiklian thanked people in those suburbs for booking jabs. 

But freedom is on the horizon with more vaccinations reported on Tuesday moving the state closer to the 70 per cent target to end the lockdown.

The premier on Monday promised to reward double-jabbed residents with a 'new freedom' in September for reaching the state's first vaccination target - most likely to be haircuts.

Ms Berejiklian also appears poised to end the lockdown, now in its ninth week, when the state hits 70 per cent vaccination in October. 

Doherty Institute Director Professor Sharon Lewin confirmed modelling that the government is relying on to end the relentless cycle of lockdowns does not depend on the number of infections circulating in the community. 

'Zero-Covid is no longer the goal once you have 70 to 80 per cent of people vaccinated. Whether you start at 30 cases or 800 cases you can still open up safely,' she told ABC's The Drum on Monday.

'With 70 per cent vaccination you will get hundreds of thousands of cases, even starting from 30 cases. However, in the presence of vaccination, your deaths and hospitalisations will be greatly reduced.' 

NSW has now exceeded the record number of daily cases set by Victoria at the height of its second wave last year. Pictured: Women exercising in Sydney on Monday

Debate on how to interpret the Institute's roadmap out of lockdowns and interstate border closures has been fiercely debated by governments of Queensland, Victoria and Western Australia who have voiced opposition about reopening amid spiralling cases.

For weeks now Ms Berejiklian has repeatedly promised that extra freedoms would be given when NSW completes six million jabs, with that milestone likely to be confirmed on Tuesday, prompting expectations of at least a small relaxation of the rules.

The premier confirmed such a plan was in the works on Monday night during a TV interview blitz, her first since the outbreak started on June 16.

NSW had completed more than 5.9 million jabs on Monday, meaning the six million target would be reached a week earlier than scheduled after a huge vaccination drive, particularly in south-west Sydney where daily Covid cases are in the hundreds.

Pictured: People arriving at the vaccination hub in Homebush, Sydney, on Monday August 23

Speaking to the Nine Network on Tuesday, Prime Minister Scott Morrison said his home state had managed to keep cases low - as it had to - while vaccination rates ramped up.

'Overseas they've got tens of thousands of cases every day,' he said.

'I was talking to Boris Johnson the other day (and) he's amazed that our cases are that low. It's all relative.'

A record 738,000 people were vaccinated in NSW last week, with 5.9 million jabs to date.

Ms Berejiklian has previously flagged increased freedoms for fully vaccinated residents once NSW records six million vaccinations.

With that total to be reached on Tuesday, Ms Berejiklian on Monday night said the government would offer 'at least one' eased restriction on residents who are fully vaccinated.

She did not outline what that would be, saying it was still being worked out by health authorities, but it would come by week's end.

Real freedom will not come until 70 per cent of the state's population is fully vaccinated

'In NSW, we are likely to have that (rate) at the end of October and hit 80 per cent - which gives us life before the outbreak, pretty much life as we knew it - in the middle of November,' she told the Nine Network.

Lockdown will remain in place until at least August 28 in regional NSW and at least September 30 in Sydney and surrounds.

Ms Berejiklian acknowledged her government had underestimated the virulence of the Delta strain, electing to avoid an immediate lockdown when it first appeared in Bondi in mid-June.

But she reiterated all governments would eventually need to tolerate COVID-19 in the community as 'we can't live like hermits forever'.

'I am very up front about being held accountable, I lead the government, but we base all the decisions on the best advice at the time. We will not be perfect,' Ms Berejiklian said.