Four weeks on from discovering the northern beaches outbreak, NSW Health is still trying to link 14 recent coronavirus cases to known clusters.

Five locally acquired coronavirus cases were reported on Tuesday in NSW from just under 15,000 tests.

The origins of two new cases – one on the northern beaches and one in Blacktown – are so far unknown.

All up, 12 cases found since December 16 are still being investigated by NSW contact tracers, including three detected before Christmas.

A further two cases – from the Canterbury-Bankstown and Lane Cove council areas – have been fully investigated without any link found.

NSW Premier Gladys Berejiklian said it was unlikely any restrictions in Greater Sydney would be eased this week, and mandatory mask usage would not change in the near future.

“We’re still seeing community transmission,” she told reporters on Tuesday.

“Even though in most instances, (they are) household contacts or people already in isolation, but we have had a couple of examples where they’re still unlinked, and that’s always a concern.”

She again backed her state’s contact tracing teams, saying their work enabled the government to make decisions that didn’t place “unnecessary burdens” on residents, such as keeping interstate borders open.

She also said the search to identify the case that sparked the northern beaches outbreak would not cease.

“We never give up the hunt in NSW,” she said.

“Sometimes it might take us hours, sometimes days, or sometimes weeks, but we always get to the bottom of what we think happened, and I’m confident we’ll get there.

“But we also have to give our experts time to make those connections.”

Testing numbers reported on Tuesday were again below that of the day before, concerning NSW officials.

Daily testing figures fell as low as 6173 before the northern beaches outbreak was discovered.

“We need 25,000-plus tests a day and we particularly need to see testing in places such as the northern beaches, such as western Sydney where we’ve seen cases recently,” NSW Health’s Jeremy McAnulty said.

NSW has more than 200 active coronavirus cases, including one person who is in hospital in intensive care.

Alerts remain out for dozens of hotspots, including a shopping centre in Warriewood, a post office in Hurlstone Park and a workers club in Blacktown.

A casual-contact alert was on Tuesday evening also issued for The Groomsmen Barber Shop on January 6, which is inside the Warriewood shopping centre already subject to health alerts.

Meanwhile, the ACT and Northern Territory have lifted travel restrictions for the Central Coast, Wollongong and some parts of Greater Sydney.

-AAP