NSW Premier Gladys Berejiklian has stopped short of making face coverings mandatory, as they will be in Melbourne and Mitchell Shire from Thursday.
Prime Minister Scott Morrison backed the Victorian and NSW governments' approach.
"The situation in Sydney in particular, and NSW more broadly, is not the situation in Melbourne. It could not be more different," he told 2GB radio.
He wore a mask during a medical appointment recently and has no qualms about being seen with a face covering in public.
"If the medical advice wherever I am requires me to do so, of course I would," Mr Morrison said.
Dr Bartone said international and domestic border closures had been successful in slowing the early spread of coronavirus.
"The national cabinet should now strengthen controls at all domestic borders," he said.
"Border closure works. If existing border closures were relaxed, it would create a risk of the virus returning."
NSW will toughen its border restrictions on people wanting to enter from Victoria from Wednesday.
Queensland is considering expanding its blacklist of NSW virus hotspots.
The move comes after two women were caught trying to smuggle a man with no entry permit across the Queensland border.
Victoria recorded another 374 cases on Tuesday and three more people died.
NSW confirmed 16 new cases on Wednesday, just one of whom was in hotel quarantine.
People in Australia must stay at least 1.5 metres away from others. Check your state’s restrictions on gathering limits.
If you are experiencing cold or flu symptoms, stay home and arrange a test by calling your doctor or contact the Coronavirus Health Information Hotline on 1800 020 080.
News and information is available in 63 languages at sbs.com.au/coronavirus