Victoria state of which Melbourne is the capital has recorded double digit rises in new Covid-19 infections, accounting for nearly 90% of the 126 cases detected nationally over the past week.
"At the moment the recommendation is simply an advisory, a strong advisory, where what we don't want is people to come from those areas to other parts of Victoria, or interstate," Australia's Chief Medical Officer Brendan Murphy told Australian Broadcasting Corp radio.
"If you are coming from interstate and you have family in one of those areas, we would prefer you not to come and visit that area and potentially take the virus back."
The Victorian government has said it would reimpose restrictions on social gatherings after the surge in new cases it says has been caused by family get-togethers attended by people with mild symptoms.
Officials have also criticised people who have gone shopping while awaiting Covid-19 test results.
New South Wales, Australia's most populous state, told residents to avoid travelling to hotspots in neighbouring Victoria as the winter school holidays approach.
"We're asking people to consider their trips to Melbourne as community transmission at the moment is higher than what they would like," NSW Premier Gladys Berejiklian told reporters in Sydney.
Despite the spike in cases in Victoria, Prime Minister Scott Morrison urged states and territories to continue removing the bulk of social distancing restrictions by the end of July.
"We have to ensure that we can run our economy, run our lives, run our communities alongside this virus," Morrison told reporters in Sydney.
