Australia's economic recovery hinges on COVID suppression but the opposition is warning of what a sluggish vaccination rollout means for future freedom.

Australia's border will stay shut until 2022 as the federal government targets COVID suppression, while the opposition says a sluggish vaccination rollout will affect future freedom.

The "tragic" events in India are a reminder of the threat still posed by the virus and there will be an assumption in this week's budget of borders opening next year, Treasurer Josh Frydenberg says.

"We don't move ahead of the health advice. We've got to ensure that our communities stay safe and when we suppress the virus as we've successfully done, our economy recovers," he told the ABC on Sunday.

But with the vaccination rollout running at "about 350,000 doses per week", Australia's adult population won't be fully vaccinated until 2023, opposition health spokesman Mark Butler says.

"Three weeks ago Scott Morrison said there could be international travel and home quarantine by as early as July," Mr Butler told reporters.

"This morning ... he's saying Australia will be locked down forever."

The prime minister said Australia would continue to record new cases from overseas arrivals and the borders will only open when it's safe.

"Australians are living like in few countries around the world today," he posted on Facebook.

"We will continue to do everything we can to work together, prevent a third wave and roll out our vaccination programme."

New Zealand's suspension of quarantine-free travel with NSW lifts at midnight on Sunday.

Initially shut down after two local cases in Sydney, NZ COVID-19 Minister Chris Hipkins said he was satisfied travel could resume following no evidence of "widespread undetected community transmission".

NSW recorded zero new locally acquired COVID-19 cases in the 24 hours to 8pm on Saturday.

Travel beyond Australia's border is expected to happen in stages as more travel bubbles open with safe countries, Health Minister Greg Hunt said.

"Our goal is very simple: to progressively open as quickly as we can, subject to safety," he said on Sunday.

"Green lanes, vaccinations and then the potential for those that have been vaccinated to be able to travel and return in different circumstances."

There are encouraging signs the government's approach is working despite criticism "the sky would fall in" when the JobKeeper incentive wound up, Mr Frydenberg said.

"We haven't seen that cliff that some people were predicting."

His comments come as Anglicare Australia says many renters are becoming homeless as a result of eviction moratoriums and rent deferrals coming to an end.

A survey of 10 of the charity's member agencies shows many people still need the rental relief measures that carried them through the pandemic.

While in most parts of the country eviction moratoriums and rental arrears have ended, many renters have also had their JobSeeker payments cut, according to Anglicare executive director Kasy Chambers.

"This is a perfect storm," she said.

Meanwhile, NSW Health is still unclear how an infected east Sydney man caught the virus, which shared the same genomic sequencing as a returned traveller from the US in quarantine.

Most current coronavirus-related restrictions across Greater Sydney will be extended for another week except for mask use in retail settings.

Retail customers are no longer obliged to wear masks but staff must continue to.