Federal Health Minister Greg Hunt has seized on Melbourne’s run of low virus numbers to again urge the Victorian government to wind back coronavirus restrictions.

“They can, we believe, take safe steps forward, which will help improve mental health,” Mr Hunt told Sky News.

Victoria had 10 new COVID cases on Tuesday – continuing a run for the past week of fewer than 20 infections, including a day of just five on Monday.

The recent trend has dropped Melbourne’s key 14-day average of new cases below 20 for the first time in months, to 18.2. The figure for country Victoria – where there have been few cases in the past week – remains at 0.6.

The majority of Victoria’s recent new cases have been linked to known outbreaks – although seven from Tuesday remain under investigation.

• NSW celebrates fourth consecutive day without community transmission

With community transmission of the virus slowing in Victoria and all but grinding to a halt elsewhere in Australia, Mr Hunt said the time was right to do away with state border restrictions.

“We think the epidemiology in Australia is so strong now that it’s a COVID-safe country,” he said.

Mr Hunt’s renewed push came as the world reached a grim COVID milestone. Johns Hopkins University said it had clocked more than one million deaths from COVID-19 since the pandemic began – to be exact, 1,000,555 deaths. There have been 33,273,720 confirmed cases globally.

But, while conceding Melbourne’s progress is “pleasing”, Premier Daniel Andrews remained determined that the city’s virus measures would not change significantly before October 19 – and then only if the benchmark 14-day average is below five cases.

“The last thing is, just as Melbourne is on the cusp of coming down to acceptable levels to allow us to open up more, to have this
take a run in regional Victoria would be … that’s exactly what we’re trying to avoid,” he said.

He said Victoria still had too many mystery cases to hasten the pace of easing restrictions.

“I understand that many have very strong views on this. We’ll get the place open as soon as we can safely do so,” he said.

“Too much has been given. Too much sacrifice has been made for us to take anything other than safe and steady steps.”

Melbourne’s cafes and restaurants remain takeaway only, but other virus measures have  been wound back.

On Tuesday, Mr Hunt said he was worried that the tough markers set to allow small businesses to reopen could trap owners in a cycle of opening and closing again.

“The Prime Minister, the Treasurer and myself respectfully asked Victoria to review those thresholds,” Mr Hunt said.

On Sunday, just after Mr Andrews announced the rollback of some Melbourne measures, Scott Morrison and Josh Frydenberg joined Mr Hunt in calling for the state’s timetable to be accelerated.

“We note that, at similar case levels, NSW was fundamentally open while remaining COVID-safe due to a world-class contact tracing facility,” the federal trio said in a joint statement.

“As many epidemiologists have encouraged, we would support Victoria in reviewing the trigger of five and zero cases with regards to the third and last steps.”

They said they were “deeply concerned about the mental health impacts of a prolonged lockdown on Melbourne residents”.

But Mr Andrews remained committed to his timetable.

“The strategy is delivering us the lower numbers and I think an increased sense of confidence that we are going to be able to continue to take those safe and steady steps,” he said.

Victorian authorities will be guided by case numbers as they look to further ease restrictions. But they will wait at least three weeks.

“We took a substantial step on Sunday and we are well placed to take an even more substantial step towards that COVID normal on or about 18 or 19 October,” Mr Andrews said.

Seven more deaths were also confirmed on Tuesday.

They were a man in his 60s, and another in his 70s, a woman and two men in their 80s and a woman and a man in their 90s.

Their deaths take Victoria’s COVID toll to 794 and the Australian toll to 882.