The payments - designed to compensate people who had caught COVID and had to isolate and miss work - had ended on June 30 but will now be reinstated.
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People eligible for the payments will be able to apply on Wednesday morning, either online or by calling Services Australia.
Albanese said people isolating would have to meet similar requirements for the disaster payments as before.
“This decision will result in more people going to work while they are sick and, unfortunately, will result in more people getting sick,” the Australian Council of Trade Unions assistant secretary Liam O’Brien told Yahoo Finance Australia earlier in the week.
Reinstating the payments until September will cost the government around $780 million, according to the PM. The cost will be split between the Commonwealth and state and territory governments.
“We've received advice based upon this surge that is occurring,” Albanese said on Saturday.
“We want to make sure that people's health is looked after, and that vulnerable people are looked after,” he said.
“And that's why I've made this positive decision today, and it's been supported by the states and territories.”
He also said the chief medical officer, professor Paul Kelly, was also recommending a return to mask-wearing indoors and in places where social distancing wasn’t possible.
Telehealth consultations for COVID antiviral medication will also continue to be covered by Medicare, according to Albanese.
The chief medical officer expects COVID infections to peak in August.