SYDNEY (REUTERS, BLOOMBERG) - Australia's New South Wales state on Thursday (July 8) reported its biggest daily rise in locally acquired cases of Covid-19 for the year as officials struggle to stamp out a growing cluster of the highly infectious Delta variant in Sydney.

New South Wales (NSW) reported 38 new local cases, up from 27 a day earlier, as its capital Sydney prepares for a third week of a lockdown.

"Those numbers are too high - we need to get those numbers down," New South Wales state Premier Gladys Berejiklian told reporters on Thursday. "Please, please avoid contact with households with other households, please avoid visiting family and friends because you are not allowed to."

Of Thursday's cases, 26 were either in isolation throughout or for part of their infectious period, while 11 spent time in the community while they were infectious. One case is under investigation.

Total infections neared 400 amid the largest outbreak of this year in the state, since the first case was detected in the city more than three weeks ago in a limousine driver who transported overseas airline crew.

A strict stay-at-home order had been enforced in Sydney, Australia's largest city and home to a fifth of the country's 25 million population, since June 26 for two weeks restricting people's movements and limiting gatherings.

That was extended on Wednesday until July 16 after restrictions failed to curtail the spread with officials frustrated after finding new infections linked to illegal gatherings and people flouting social distancing rules.

The lingering lockdown of some six million Australians during school holidays is a blow to the domestic tourism industry and yet again shows the limitations of the government's strategy of trying to eliminate community transmission of the virus.

While economies such as Britain and the United States are preparing to open up, Australia's international borders remain largely closed to non-residents and comparatively small clusters of the coronavirus make even domestic travel difficult as states and territories pull up the drawbridge.

Along with the Delta variant increasingly leaking out of the nation's hotel-quarantine system, a sluggish vaccine roll-out is being blamed for the ongoing disruption.

Ms Berejiklian has asked Prime Minister Scott Morrison to ramp up the vaccination roll-out that has so far seen just 26 per cent of Australians receive their first jab.

Ms Berejiklian has flagged her government may need to impose harsher restrictions in three south-western Sydney local government areas - Fairfield, Liverpool and Canterbury-Bankstown.

Those communities, with a combined population of almost one million people, have relatively high proportions of immigrant families. According to data from the most recent census, about half their populations were born overseas, often in non-English-speaking countries.

"The two biggest areas where people are spreading the virus is through household contacts of people close to them, and people who are undertaking activities with symptoms," Ms Berejiklian said.

"We don't want to prolong the lockdown, we don't want to see Sydney or New South Wales going in and out of lockdown until we have the vast majority of our population vaccinated."

Just over 9 per cent of people in NSW have been fully vaccinated, while about 29 per cent have had a first dose.

Prime Minister Scott Morrison said the federal government would ensure adequate economic support if the lockdown was extended, saying the state was on "shifting sands" and urged patience.

"I know people are getting tired ... getting frustrated. This is a virus we are dealing with, and it tends to set its own rules," Mr Morrison said during a televised media conference.

The Australian Medical Association (AMA), meanwhile, warned NSW authorities to avoid lifting any lockdown rules before totally suppressing the Delta outbreak.

"There is no alternative to elimination for New South Wales ... nowhere in the world has any community been able to live with Delta without very significant levels of vaccination," AMA President Omar Khorshid said.