Butler told The Guardian “there are going to be millions of people infected by Covid in this coming few weeks’ period”.

“We have 250,000 to 300,000 people today who are infected on official data. The real number’s probably twice that, or maybe even more, according to what we understand about this variant.”

Butler said the government wanted to keep the number “as low as possible” which is why chief health officers were strongly encouraging mask-wearing in crowded indoor spaces, but the “primary focus” was minimising the number getting “severely unwell”.

“Which is why our focus has been on boosters, on that fourth dose being made much more widely available.”

Prime Minister Anthony Albanese has insisted the federal government will work closely alongside states and territories on measures to curb Covid-19 cases amid a winter rise in infections.

As case numbers across the country spiral due to more infectious sub-variants of the virus, Albanese said Covid-19 was continuing to provide “real challenges”.

“We are encouraging, along with state and territory government, rules to be applied where commonsense applies,” he told the Seven Network on Thursday.

“If you can’t socially distance then people should consider wearing a mask, and we’ll continue to engage through the states and territories. I’m in constant contact with them.”

Queensland Premier Annastacia Palaszczuk has asked the prime minister to call a national cabinet meeting so state leaders can be briefed by the chief health officer about the deteriorating Covid-19 situation.

She said there had been an “escalation” of cases and a meeting should be held within the next few weeks.

The federal government has come under fire for its decision to end a scheme allowing concession card holders to receive 10 free rapid antigen tests every three months, as well as payments for workers needing to isolate from their job.

The prime minister has defended the decision, arguing the government had provided further support for the health sector.

“We inherited those cut offs across a range of decisions from the former government … we also inherited $1 trillion of debt,” he said.

“We have added three months’ health funding for the state and territory governments … because the pandemic continues to have an impact.”

Treasurer Jim Chalmers said the situation was challenging for many people.

“We don’t pretend it is not tough for people. Covid has been diabolical for a lot of people and we have tried to do the best that we can to make sure that we are supporting people,” he told the Nine Network.

“There is no use pretending that we can continue these programs with the severe budget constraints that we have got.”

Meanwhile, a cruise ship carrying more than 120 confirmed cases of Covid-19 will return to Brisbane after making two scheduled stops in NSW.

The majority of cases on board the Coral Princess are among crew members, while around 10 Covid-positive passengers were prevented from disembarking in Sydney on Wednesday.

The ship, which has 2300 passengers and crew aboard, is due to return to its home port of Brisbane on Thursday. Some 24 infected passengers left the vessel before it departed Brisbane on Sunday.

The ship was assessed by NSW Health as it travelled through the state’s waters as having an “amber” Covid-19 risk level, the second highest.

People who tested positive on board were likely infected before they joined the ship, NSW Health said.