It came after 177 new infections were reported in the latest 24-hour period - the largest daily tally since the cluster was discovered in mid-June.
"I am as upset and frustrated as all of you that we were not able to get the case numbers we would have liked at this point in time but that is the reality," state Premier Gladys Berejiklian told reporters.
More than 2,500 people have been infected in a cluster that began when a limousine driver tested positive on June 16 to the contagious Delta variant. The driver had been infected by a US aircrew he transported from Sydney airport.
The death toll from the cluster reached 11 on Wednesday with a woman in her 90s dying in a Sydney hospital.
An already protracted stay-at-home order has failed to douse the Covid-19 outbreak, with authorities warning of tougher policing to stamp out non-compliance.
Of particular concern, at least 46 of the new cases were people active in the community before being diagnosed, raising the likelihood of transmission.
Authorities have cautioned that active community transmission must be near zero before rules are relaxed.
Ms Berejiklian added police would boost enforcement of wide-ranging social distancing rules and urged people to report suspected wrongdoing, saying “we cannot put up with people continuing to do the wrong thing because it is setting us all back”.
In one case, a mourning ceremony attended by 50 people in violation of lockdown rules resulted in 45 infections, she said.
The extension turns what was initially intended to be a "snap" lockdown of Australia's most populous city into one of the country's longest since the start of the pandemic, and may spark the second recession national economy in two years, according to economists.
To minimise the economic impact, the NSW government said it would lift a ban on non-occupied construction in most of Sydney. However, it expanded a list of local government areas within the city where the ban would stay because of the prevalence of Covid-19 cases there.
The NSW government said it was redirecting Pfizer vaccine doses, which have so far been restricted to people aged 40-60, from relatively unaffected regional areas to final-year school students in the worst-affected Sydney neighbourhoods.
In contrast to New South Wales, the states of Victoria and South Australia on Wednesday began their first day out of shorter lockdowns that halted outbreaks there. Victoria reported eight new cases, all of them isolated throughout their infectious period, and another case still under investigation.
Australia has kept its Covid-19 numbers relatively low, with just over 33,200 cases and 921 deaths, out of a population of about 25 million, since the pandemic began.