The federal government wants to ensure people of all cultures get vaccinated against the coronavirus, while Labor is wondering when anyone will get the jab.
Health Minister Greg Hunt said it is critical that communications around the vaccine program are also targeted for culturally, ethnically, and linguistically diverse communities.
"The government recognises that people from multicultural communities are a significant part of the health, aged care, child care and disability workforce and will be among the first people in Australia to receive vaccinations," Mr Hunt said in a statement on Sunday.
But shadow treasurer Jim Chalmers is concerned that Australia is languishing in rolling out the program, which is creating uncertainty in communities and the economy more broadly.
He said some 90 countries have their vaccinations program under way.
"After the prime minister said we were at the front of the queue 160 million people have been vaccinated around the world, while zero Australians have been vaccinated," Dr Chalmers told Sky News' Sunday Agenda program.
The Australian roll-out is not due until later this month.
Meanwhile, Victorian Premier Daniel Andrews is gearing up to lead a re-think of Australia's hotel quarantine program in light of the UK strain of coronavirus which now has his contact tracers in a frenzy.
On Saturday Mr Andrews said he had asked his health experts to do a risk assessment of the "fast-moving" disease, which would form his position in a national discussion about hotel quarantine and when the vaccine is rolled out.
The Morrison government remains in continuing discussions with the Northern Territory to expand the Howard Springs quarantine facility, having already expanded its capacity to 850.
"It's been obvious for sometime, certainly some months, that there has needed to be an expansion of federal facilities like this one," Dr Chalmers said.
"It hasn't come soon enough to prevent those 40,000 Australians overseas, despite the prime minister's promise to get people home by Christmas."
Victoria paused all international passenger flights from Saturday as part of its five-day statewide lockdown as health authorities attempt to ring-fence an outbreak of the infectious UK variant of the virus.
The state recorded two new local cases and a third in hotel quarantine on Saturday.
Victoria's health department listed four new exposure sites on Sunday morning. They are two Pascoe Vale swimming pools, and a Woolworths and bakery in Broadmeadows.
The state has 14 cases linked to the Holiday Inn outbreak.
In South Australia, the government has responded to its own cluster following a quarantine leak in late 2020 by opening a new facility for overseas travellers and locals who test positive for the virus.
Ahead of a tour of the 72-bed medi-hotel at Tom's Court Hotel in Adelaide, South Australian Health Minister Stephen Wade said it was the only COVID-positive facility in Australia.
"It delivers what we believe is the best model in Australia for the management of COVID-positive people," Mr Wade said on Sunday.
Work has been performed at the hotel to improve ventilation to minimise the risk of airborne transmission, and there is additional CCTV to reduce floor movement.
It will be staffed by SA Health and SA Police staff and will open on Monday.
NSW and Queensland on Sunday reported no new local cases. It was the 28th consecutive day in NSW without local cases - the longest stretch since the pandemic began.
Victorian visitors to NSW are obliged to follow their home state's "stay at home" orders. This does not apply to residents of NSW border communities unless they have visited Greater Melbourne.
NSW has strongly advised residents to avoid non-essential travel to Victoria.
Tasmania, Northern Territory, Queensland, WA and SA have closed their borders to Victorian travellers.
