Federal health officials are under pressure to accelerate the rollout of COVID booster shots to as fast as three months after a second dose, to combat the spread of the virulent Omicron variant.

Health Minister Greg Hunt says there’s no indication state governments will reimpose lockdowns, but some premiers are reintroducing mask rules, with one of the Commonwealth’s leading health experts recommending all Australians use them in crowded indoor spaces like shops.

“We don’t see that’s a likely situation in Australia,” Mr Hunt said on Sunday, when asked if the nation would again experience lockdowns.

“We are well prepared and people are overwhelmingly, I have to say, continuing to do an amazing job.”

New South Wales logged another record 2566 COVID cases on Sunday, with the state’s health department saying the Omicron variant “likely accounts for the majority”.

However, despite some 11,000 cases in the past week, just 227 people are in hospital and only 28 in intensive care.

NSW Health Minister Brad Hazzard. Photo: AAP

Hospitalisations ticked up by 20 from the previous day.

NSW Premier Dominic Perrottet said he believed the state was in a “strong place” considering its vaccination rate of 93.4 per cent of people over 16, and said further restrictions were not currently on the cards.

His Liberal government has come under fire from some doctors and commentators for removing mask mandates and QR check-ins only last week, with some calling for those rules to be reinstated.

Mr Perrottet said the government “strongly encouraged” mask wearing, but declined to make them mandatory in public again.

“This is all about taking personal responsibility … The government can’t do everything. It’s over to the people of our state,” he said.

NSW Health Minister Brad Hazzard, however, gave the strongest call yet from a politician for the timing of booster shots to be brought forward.

Federal health regulator ATAGI recently accelerated the timetable for boosters from six months to five months after a second dose, but on Friday declined to bring that any further forward.

Mr Hazzard said he wanted the gap decreased to three or four months, to allow more people to get boosters faster.

“It would be better to have a shorter period than has currently been dictated,” he said.

“I would like to see ATAGI shorten the period.”

As of Sunday, more than 1.328 million Australians had received a third shot of COVID vaccine, according to federal statistics.

On Saturday, Prime Minister Scott Morrison said nearly three million people were eligible for boosters.

Boosters are essential, according to doctors, with two shots of vaccine showing less efficacy against the Omicron variant.

Mr Morrison last week flagged the possibility of ATAGI shortening the booster interval to four months.

He said the timing was “under constant review”, and that there was more than one million booster shots sitting in the distribution system – including pharmacies – across the country.

Mr Hunt said on Sunday that more than five million doses would be “pre-positioned” to be administered over the Christmas period, with another two million doses expected to arrive in the country from overseas in coming days.

Tweet from @GregHuntMP

The Health Minister was asked by journalists about European nations like the Netherlands entering lockdowns over Omicron concerns.

Mr Hunt said Australia was not in the same position, considering our summer versus a European winter danger period for COVID, and high vaccination rates, and said he didn’t expect state governments to reintroduce heavy health measures.

“None of the states or territories have indicated that at this point in time. Obviously, everyone looks and responds to the circumstances. The direction of Australia is overwhelmingly towards opening up,” Mr Hunt said.

“Individual measures might be adjusted from time to time depending on circumstances. But the clear direction is higher vaccination and less restrictions.”

Tasmania on Sunday reintroduced mask mandates indoors.

Dr Sonya Bennett, the federal deputy chief medical officer, recommended all Australians wear masks in crowded indoor spaces like shops, even when it was not mandatory to do so.

Deputy CMO Dr Sonya Bennett. Photo: AAP

“It’s a simple, easy thing to do. We know at Christmas time the shops do get very crowded,” she said.

“My plea to the community is we don’t need to wait for mandates to tell us what is sensible to do. That particularly applies to masks.”

Dr Bennett also urged people to maintain basic COVID safety behaviours like social distancing, hand hygiene and staying home when unwell.

“If you’re having gatherings, think about having them outdoors or in well-ventilated spaces. Limit numbers,” she said.

“Our systems are well prepared. We’re a highly vaccinated population, one of the highest rates of coverage in the world. But the numbers, the transmission rate alone is concerning.”

Mr Morrison this weekend said Australia was “past the time when we just talk about case numbers”, saying people should focus on numbers of serious illness instead of raw transmission rates.

“It is a leading indicator on some issues, but the real issue is how many people are experiencing serious illness,” he said on Saturday.

“What matters is hospitalisations, ICU, people on ventilators and severe illness.”