Mr Hazzard said he is troubled by the ongoing increase in daily infections.
"[Today's numbers] takes us up from the previous day, which was 136 cases, and, of course, it was only a few days ago that we were in the 70s. So what it is telling us is we have a continuing and growing problem, particularly in south-west and western Sydney," he told reporters on Saturday.
The new infections announced on Saturday came from a record 93,910 tests, compared to the previous day’s total of 86,620.
The death of a man in his 80s from south-west Sydney announced on Friday was officially included in Saturday's numbers. The death toll from the current outbreak is now six.
NSW records 163 new local COVID-19 cases as numbers continue to rise
"We express our condolences to the man's family," NSW Deputy Chief Health Officer Jeremy McAnulty said.
Greater Sydney remains in lockdown until at least 30 July and three local government areas in regional NSW are under stay-at-home orders until at least 28 July as authorities battle to contain an outbreak of the Delta variant.
Mr Hazzard said the new cases were mainly in the areas of Fairfield, Canterbury-Bankstown, Cumberland, Blacktown and Liverpool.
He urged people, particularly in those hotspots, to avoid contact with other people and stay home.
"Hear the message and stay at home. Don't intermingle with members of other households. It will continue to cause grief in western and southwestern Sydney. Just please, stop doing it," he said.
NSW to receive 50,000 additional Pfizer doses
Deputy chief medical officer Michael Kidd has confirmed that a shipment of additional Pfizer vaccines will be delivered to NSW this week.
Professor Kidd said the extra 50,000 Pfizer doses are coming from a yet unallocated supply from the so-called national stockpile.
"The Commonwealth will increase the emergency allocation to NSW of additional doses of Pfizer from 150,000 to 200,000 doses this week," he said on Saturday afternoon.
"The Commonwealth will constantly assess requests against any reserves held by the Commonwealth."
The announcement came after Mr Hazzard urged other state leaders to reconsider their refusal to divert Pfizer vaccines to NSW to boost vaccination rates in western and south-western Sydney.
States and territories pushed back against the NSW government's pleas at national cabinet on Friday to assist by sending Pfizer jabs.
"It is with disappointment that I heard some of the responses from leaders from other states," Mr Hazzard said on Saturday.
"I can't quite see the difference between beating backfires and beating back and addressing the problems of floods, and beating back this COVID virus.
"I want to remind those other states and territories that last time I looked, we were a 'Common-wealth', we work together."
NSW declares 'national emergency' as COVID-19 numbers grow
Mr Hazzard said he has found it "frustrating" communicating with the federal government on vaccine supply and the expected delivery schedule of vaccine supplies.
"At the moment it is like fighting a war with both arms behind your back," he said.
Chris Moy, Vice President of the Australian Medical Association, said he is concerned that the strategies employed so far have not reduced the number of new cases.
"Unfortunately, the ability for Sydney to come back from this is looking more and more remote with the numbers going up. And that means unfortunately that Sydney is almost going to go into a different mode," he said.
"Where Sydney may be, unfortunately, is that the lockdown will have to continue, but not to squash it, but just to keep the numbers within a reasonable band to protect the community, but also stop hospitals for example, from being overrun."
Police says deliberate house parties and gatherings must stop
In the past 24 hours, NSW Police issued 246 fines to people for breaching COVID-19 public health orders.
NSW Police deputy commissioner, Gary Worboys, said it is reprehensible that people continue to deliberately breach COVID-19 rules.
"The hard part for everyone to get their head around is the fact that this Delta strain is so transmissible, that people will quite consciously invite people into their house and each and every one of those people then returns to their home with the prospect of infecting everyone in their household," he said on Saturday.
"This sort of behaviour is highly irresponsible, and is quite conscious in terms of that people are actually planning these events and inviting people around."
Deputy Commissioner Worboys said additional officers are being deployed to monitor a planned protest against the lockdown and vaccines on Saturday.
Mr Hazzard said he supports the right to protest, but said doing so right now is not appropriate.
"At the present time we've got cases going through the roof, and we have people thinking that it's okay to get out there and possibly be close to each other at a demonstration. I just think that's a bit silly," he said.
Focus on improved messaging in western Sydney
Mr Hazzard said the government is continuing to work with community leaders to improve communication of messages to multicultural communities in western Sydney.
"We are a very multicultural society in south-west and western Sydney and it is one of the joys of this nation that we are a proud multicultural nation. But sometimes, people who have come from overseas perhaps have suffered at the hands of other governments and perhaps getting the messages through is challenging," he said.
"My focus is not on increased penalties; it is about just making sure that people understand that the most dangerous thing you can do in a pandemic is to be near another human being."
He dismissed suggestions from Victorian Premier Daniel Andrews of a "ring of steel" approach around Sydney.
"I don't see that as being the appropriate approach," he said. "We already have limits in terms of workers being able to come out of the five most challenged local government areas at the present time. So I think that's very appropriate as to the balance that we've struck to date."
New restrictions commence
New restrictions have come into effect for the local government areas of Cumberland and Blacktown.
Residents in these areas will only be allowed to leave their LGA if they are an authorised worker. Currently, they are not subject to a requirement to get a COVID-19 test every three days.
NSW Health said it is concerned by the detection of virus fragments in wastewater in the Southern Highlands.
"There are no known cases in this area, which is of great concern," the department said.
Residents are being urged to monitor for COVID-19 symptoms and to get tested and isolate if symptoms do appear.
The list of exposure sites has also been updated to include locations in Belmore, Lakemba and Wollongong.
Over a 24-hour period until 8pm 23 July, 25,312 vaccine doses were administered, taking the overall number of doses delivered to 1,309,786.