The state reported another 30 cases in the 24 hours to 8pm on Saturday with 28 linked to the cluster on Sydney’s northern beaches.

The total number of known coronavirus cases in NSW has now risen to 70, though the state’s leader remained optimistic about containing the outbreak.

“The one positive is we still have not seen evidence of massive seeding outside the northern beaches community and our aim, of course, is to keep that in place,” NSW Premier Gladys Berejiklian told reporters on Sunday.

The government has imposed a number of restrictions on the Sydney region, including the Blue Mountains, Central Coast and Illawarra-Shoalhaven, which will remain in place until 11.59pm Wednesday.

No more than 10 people are allowed at household gatherings and patrons will need to maintain a four-square metre distancing at venues.

Up to 300 people will be permitted at places of worship and hospitality venues, while singing and chanting at indoor venues is banned, and dance floors will only be allowed at weddings.

People are also being urged to wear masks until Wednesday and to avoid visiting any vulnerable friends, relatives or aged-care facilities until Christmas Eve.

Health Minister Brad Hazzard said the restrictions balance the public health interest with the need to keep the economy open.

“You can safely say that NSW leads the country in keeping jobs and keeping the economy moving, and keeping people safe,” he said.

“We have diamond-level health tracers, and I think the work that we have done over that period has been a very balanced way of approaching this.”

NSW Chief Health Officer Dr Kerry Chant said contact tracers are yet to locate patient zero, but an extensive investigation is underway.

She said no one who has been granted quarantine exemptions, including international flight crews, had tested positive for the virus.

However, Chant conceded that contact tracers may never be able to find patient zero.

“While we really do want to find the source, it may be that this is going to be a challenge beyond us, but we are doing everything we can,” Chant said.

Amid concerns about the growing cluster, all states and territories announced they would shut their borders to Greater Sydney.

Some also barred the Central Coast, and Illawarra/Shoalhaven regions.

Sydney’s northern beaches remains the centre of the cluster, but NSW Health’s new list of cases on Sunday morning showed the virus had spread further in the city.

There are new cases are in Hornsby, Hunters Hill, Ku-ring-gai and North Sydney.

There are public health alerts for various northern beaches venues and businesses in Avalon, Belrose, Brookvale, Dee Why, Mona Vale, Narrabeen, Newport, North Narrabeen and Palm Beach.

Warnings have been issued for locations in Artarmon, Bondi Junction, Cronulla, Darling Point, Erskineville, Eveleigh, Homebush, Kirribilli, Lane Cove, Newtown, Peakhurst, Penrith, St Peters, Riverstone, Rosebury, Surry Hills, Terry Hills, Turramurra and Woolloomooloo.

Outside Sydney, Forster and Raymond Terrace are also on the warning list.

Northern beaches residents remain under stay-at-home orders last imposed back in March at the height of the COVID-19 crisis.

People are permitted to leave their homes for five basic reasons: to seek medical care, exercise, grocery shop, work or for compassionate care reasons.