The NSW premier said transmission of the virulent Delta strain was still highest in the eight local government areas in the city's west and south-west living under tightened lockdown rules.
Authorities have yet to find the source of infection for 111 of the new cases.
There are now 250 patients suffering from Covid-19 in NSW hospitals, including 53 in intensive care and 20 who require ventilation.
Ms Berejiklian on Tuesday said she wanted six million jabs in arms across NSW by the end of August - which would mean half the state's eligible population have received either their first or second jab of a Covid-19 vaccination.
She said reaching that target would give her 'additional options' in terms of easing the strict stay-at-home lockdown in Greater Sydney - which is entering its sixth week and was last week extended until at least August 29.
'We're at 3.9 million [total vaccinations in NSW]. I suspect we'll be at four million by the end of the week,' she said.
The state leader also suggested her government was considering allowing NSW residents who are vaccinated greater freedoms than those who haven't had the jab.
'We know that people value their freedom, their desire to go back to work, their desire to engage in community life,' she said.
'We want our citizens to know that if they're vaccinated and their loved ones are vaccinated, there will be opportunities for greater freedom moving forward.'
NSW Chief Health Officer Dr Kerry Chant said 43 of the 53 Covid-19 patients in the state's intensive care units were not vaccinated - underlining the need for all age groups to get the jab.
Pictured are pedestrians wearing masks in Newtown in Sydney's inner-west. The city is entering its sixth week of a strict stay-at-home lockdown
A Pfizer vaccine is administered at a Covid-19 vaccination hub in Sydney last month. NSW Premier Gladys Berejiklian on Tuesday said she wanted six million jabs in arms across NSW by the end of August
'It's tragic that we've got still people in their 60s, 70s, 80s and 90s that are unprotected,' she said.
The warning came as a cluster of cases at the Wyoming Residential Aged Care Facility in Summer Hill in Sydney's inner-west grew to 20 cases - including 18 residents and two staff members.
Six of Tuesday's newly-acquired cases are linked to the care home.
NSW Health said 73 of the new cases reported to 8pm on Monday night were found in south-west Sydney, while 67 were detected in the west and 35 in the central Sydney local health district.
Health officials also found 12 cases in the Nepean Blue Mountains region west of the city in an alarming sign the outbreak could have spilled into regional NSW.
Meanwhile, worrying new modelling overnight suggested there could be 600 new cases in Sydney each day by Friday if lockdown restrictions are not tightened across the city.
Infections could even hit an astonishing 7,700 cases a day in a worst case scenario by the end of August, experts predicted, similar to the thousands of daily cases seen overseas with the Indian Delta variant.
Authorities have yet to find the source of infection for 111 of Tuesday's 199 new cases of Covid-19
Evidence collated by Professors Allan Saul, Brendan Crabb AC, Margaret Hellard AM and Dr Campbell Aitken of the Burnet Institute on Monday showed tighter measures in the hotspot government areas may be working - but the rest of Sydney is teetering on a knife's edge.
This was clear in a late night drop of exposure sites released on Monday, including a Coles and Aldi on the city's lower north shore, as well as an auto parts store in Rockdale.
Using analysis of what restrictions did and didn't work during Melbourne's outbreak last year, the team of scientists found NSW's effective contact tracing, use of QR codes and record testing rates had helped stop the outbreak spiralling into thousands of daily cases.
Without such measures, and a lockdown, Sydney could already be looking at 1,000 daily cases - but infections are still doubling on average every nine days.
But the modelling, based on how infections have spread to date, still predicted the city would see 570 cases per day by Friday.
Health workers take out stretchers from an ambulance at the Wyoming Residential Aged Care Facility in Summers Hill on Monday. Researchers have predicted Sydney's lockdown could get much worse
Pictured are masked pedestrians in Fairfield on Tuesday morning. The Fairfield LGA is one of eight parts of Sydney under tighter stay-at-home restrictions to slow the spread of the Delta variant
This is despite south-west Sydney's outbreak slowly coming under control, with infections still increasing rapidly in other areas of the city.
The upward trend of daily cases in south-west Sydney's Fairfield reversed on July 15, six days after the three initial LGAs restrictions were tightened.
Cumberland, Blacktown, Parramatta, Georges River and Campbelltown were added to the list of LGAs under stricter lockdowns on Friday and experts are hoping the numbers drop in those areas, but they say the restrictions should be broadened.
Victoria records four new Covid cases as the state tightens its border bubble with New South Wales
Victoria has reported four new local Covid cases as the residents along the state's northern border prepare for a bubble crackdown.
All cases are linked to Victoria's current outbreaks and were in isolation for their entire infectious period. Another infection was detected in a returned traveller in hotel quarantine.
It comes as Victoria bans non-essential movement across state lines because of the hovering threat of Sydney's Covid-19 Delta variant outbreak.
From 11.59pm on Tuesday, border-bubble residents will only be able to state-hop for six reasons including medical care, compassionate purposes, work, education, playing sport or getting vaccinated.
Victoria recorded four new cases of Covid-19 on Tuesday, all of which are linked to known outbreaks. Pictured: A woman walks through Melbourne
The new measure applies to residents on both sides of the NSW-Victorian border, who must also not travel any further than necessary for that specific purpose.
Anyone caught crossing the border for a non-essential reason could face a $5452 fine.
Health Minister Martin Foley said the move would burden people in border towns, but it was vital to keeping the virus out of the state.
'With the outbreak in New South Wales still growing, the public health advice is clear: we need to limit unessential movement across the border into Victoria where it is practical and possible,' he said.
Of the 207 new infections New South Wales recorded on Monday, 83 were found in the city's south-west. Pictured: health workers at Hardi Aged Care Nursing Home Facility at Summer Hill on August 2
FIND THE LATEST EXPOSURE SITES NEAR YOU
'Although the number of cases is still lower outside south west Sydney, daily cases in the rest of Sydney are now increasing at about the same rate as happened initially in Fairfield – doubling every four to five days,' the research body said.
'Unless new controls introduced on July 28 or 30 or in the future have a major impact, our model projects that Sydney will have about 7,700 cases per day four weeks from now.'
The experts recommended bringing in 'consistent stringent restrictions', like those seen in the hotspot LGAs, all across the city.
Australian Defence Force troops have joined NSW police patrolling streets in Sydney's west and southwest during lockdown (pictured, personnel in the city on Monday)
'Not only is this the equitable approach, but epidemiologically sound,' the report concluded.
According to their modelling, it will take until the end of September to get below five new cases per day over a seven-day period.
Some areas not included in the tightened restrictions, such as Burwood, Strathfield and Bayside, are seeing higher case numbers per capita than those under the stricter lockdown.
Of the 207 new infections New South Wales recorded on Monday, 83 were found in the city's south-west - but contact tracers say those infections are contained to the area.
HOW SYDNEY'S TOUGHER LOCKDOWN RULES WILL AFFECT YOU
In the eight hotspot LGAs from 12am on Saturday, July 31 (Blacktown, Campbelltown, Canterbury-Bankstown, Cumberland, Fairfield, Georges River, Liverpool and Parramatta):
Residents must wear a mask whenever leaving the home, including when they are outdoors.
The travel limit for essential exercise and shopping has been reduced to 5km from 10km.
Those in a 'singles bubble' with another person must follow the same travel restriction.
The penalty for breaking mask restrictions will increase from $200 to $500
Police will be given the power to shut down public premises, worksites, and businesses that are caught breaching public health orders.
Worryingly, a further 53 were recorded in the west and 48 were in the central Sydney local health district.
To combat a potential explosion of cases, researchers suggested a tighter lockdown for the whole of Sydney.
'The reality is that no one is safe until everyone is safe,' the experts warned.
'Every positive case, no matter in which LGA, takes testing and contact tracing resources and has the potential to trigger new outbreaks.
The experts recommended bringing in 'consistent stringent restrictions', like those seen in the hotspot LGAs, all across the city (pictured, a runner in Bondi on Monday)
Ms Berejiklian said on Monday that at least 50 of those newly-acquired infections were out in the community while infectious. Pictured: Cleaners in personal protective equipment at Strathfield South Public School on Monday
Worrying modelling shows the virus is likely to spread even further in Sydney (pictured on Sunday) and could reach nearly 600 cases a week by Friday
Health workers take out stretchers from an ambulance at the Hardi Aged Care Nursing Home Facility in Summers Hill suburb of Sydney on August 2. There are now 232 patients suffering from Covid-19 in NSW hospitals - including 54 in intensive care and 25 who require ventilation
'A highly mobile population means new outbreaks could occur anywhere in Sydney or NSW or across Australia.'
But on a positive note, researchers found that a potential 1,000 new cases per day were avoided because movement in the city was largely curtailed near the start of the outbreak.
'We calculate that the restrictions implemented so far have avoided 4,000 cases, over and above the many prevented by contract tracing and subsequent isolation,' they said.
New exposure sites in Sydney on Monday
Anyone who attended the following venues at the dates and times listed is a close contact who must immediately get tested and isolate until a negative result is received.
Rockdale Repco 395 West Botany Street. Wednesday 28 July 10:15am to 5pm. Thursday 29 July 10am to 1pm
Anyone who attended the following venues at the dates and times listed is a casual contact who must immediately get tested and isolate until a negative result is received.
All Seasons Supermarket, Ashfield, Wednesday 28 July, 6.05pm-6.40pm
Woolworths Baulkham Hills, Wednesday 28 July, 4.15pm-4.35pm
ALDI Castle Hill, Wednesday 28 July, 5.45pm-6.05pm
Coles Castle Hill, Wednesday 28 July, 6.05pm-6.15pm
McDonald’s Castle Hill, Wednesday 28 July, 6.15pm-6.25pm
Woolworths Thornleigh, Sunday 18 July, 11.20pm-12.15pm
McDonald’s Warriewood, Wednesday 28 July, 11.45am-1pm
First Choice Liquor, Ashfield, Wednesday 28 July, 3.15pm-3.30pm
New Yen Yen Asian Supermarket, Ryde, Sunday 25 July, 12.35pm-12.40pm
Akira Sushi, Ryde, Sunday 25 July, 12.35pm-12.40pm
Australia Post Office, Kogarah, Thursday 22 July, 1.50pm-2.10pm
Tortuga Ventures, Castle Hill, Saturday 24 July, 7am-6pm
Woolworths Ryde, Top Ryde City Shopping Centre, Sunday 25 July, 12.40pm-1.15pm
Woolworths Strathfield, at the following dates and times: Sunday 25 July, 6.05pm-6.30pm; Monday 26 July, 11.50am-12.15pm; Tuesday 27 July, 1.55pm-2.20pm
Anyone who travelled on the following routes at the times listed is a close contact and must get tested and isolate for 14 days, regardless of the result.
Bus 705, From Joyce St opp Pendle Hill Station to Mandoon Rd at Girraween, Thursday 22 July, 6.20pm-6.25pm
Bus 601, From Parramatta Station, Stand A4 to Victoria Ave before Gladstone Road, Saturday 24 July, 9.26am-9.47am
Bus 601, From Victoria Ave after Carrington Road to Parramatta Station, Stand B3, Saturday 24 July, 8.47pm-9.07pm