Australia's second-biggest city Melbourne will stay locked down for a second week after reporting 20 new Covid-19 cases as it struggles to stamp out infections caused by the highly infectious Delta variant of the pandemic.

Melbourne had been due to exit the lockdown on Thursday, the sixth for its five million people in stop-start battles against the coronavirus also seen elsewhere across the country have triggered frustration and dischord.

But Victoria state Premier Dan Andrews confirmed strict stay-at-home orders will remain in place until at least August 19 after authorities were unable to trace how several of the 20 people confirmed as new cases contracted Covid-19, Reuters reports.

“If we were to open, then we would see cases akin to what is happening, tragically, in Sydney right now,” Andrews told reporters in Melbourne, referring to an outbreak in Australia's most populous city that has spread to thousands despite Sydney being in week seven of its own lockdown.