Premier Gladys Berejiklian says people should not be stopping for a chat when they leave home for essential reasons.
Ms Berejiklian was speaking at the COVID media briefing on Thursday where the Georges River, Bayside and Sutherland Shire council areas were again listed as areas of concern.
Ms Berejiklian said she was sure people were becoming "weary of the message", but it was important they realised that the Delta strain was much more contagious than earlier variants.
"Don't leave home unless you have to, don't have interaction with anyone outside your immediate household unless you absolutely have to, that's how contagious the virus is," she said.
"Even when you are going shopping to buy essential or important things, don't stop and have conversations, don't get distracted, just be very purposeful..."
NSW Health's Dr Jeremy McNulty said Georges River, Bayside and Sutherland Shire council areas were among parts of Sydney "we are particularly concerned for people to come forward for testing if they have even the mildest of symptoms".
There were 124 new, locally acquired cases of COVID-19 in the 24 hours to 8pm on Wednesday, with "at least" 48 infectious in the community.
Ms Berejiklian said she expected case numbers to rise further before they fell.
Ms Berejiklian said it would take till the weekend or early next week to see the effect of the hard lockdown.
The Premier said "a level of restrictions" would remain after July 31 when the lockdown is due to end.
"This time next week we should know what July 31 will look like," she said.
Ms Berejiklian and Dr McNulty defended contact tracers in response to questions about venue alerts being many days afterwards.
They said positive COVID cases did not always remember all the venues they had visited initially, and the list was updated as they provided new information.
Ms Berejiklian rejected suggestions contact tracers were being overwhelmed and falling behind.
She said they were "doing a phenomenal job".
Health Minister Brad Hazzard cleared up one misconception, saying people were allowed to travel to another local government area for medical reasons, including getting vaccinated.
Mr Hazzard also revealed public health orders were being amended to state that if a person claimed a medical reason for not wearing a mask, they would have to be able to have with them a letter signed by a doctor.
A new record of 85,185 people were tested in the last 24-hour period.
Ms Berejiklian said the average wait for test results was 28 hours, with priority given to advising people who had tested positive.