Hotel quarantine has been hailed as crucial in allowing the economy and community life to return to normal after the coronavirus pandemic.
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Out of the nine new cases recorded on Monday, seven were travellers returning from overseas who were compelled to isolate.
A family of four Victorians returning from Doha were on Western Australia's tally on Monday.
The two new cases in Victoria were also returned travellers and in NSW, one new case was a traveller and the other two were locally acquired.
"We continue with our border measures and the importance of those is emphasised by the fact that a significant proportion of new cases are those that show up in hotel quarantine," Health Minister Greg Hunt said.
"Border protection and hotel quarantine is literally saving lives and protecting lives, and will continue to be a fundamental part of our national health and strategic defence going forward."
Mr Hunt talked up the fact that the growth rate in cases over the past five weeks was under 0.5 per cent.
States and territories are removing restrictions at various speeds, but senior government sources believe the whole nation will be under stage three limits by the end of July.
At that time, according to Treasury, about 850,000 jobs will be restored, with interstate travel and gatherings of up to 100 people allowed.
Mr Hunt said it was highly unlikely any restrictions will be reimposed at a state level, but rather dealt with through regional, local or even facility-based lockdowns.
Public schools across NSW and Queensland have welcomed children back after about two months of most students learning from home in the latest sign Australia is edging towards a new normal.
Victoria, Tasmania and the ACT are staging staggered returns while schools in South Australia, Western Australia and the Northern Territory are already open.
Other restrictions will ease over the next week, with Victoria giving the green light to gatherings of 20 people and NSW allowing beauty salons to reopen.
The NRL is also setting the ambitious goal of opening gates to crowds from July 1.
There are 501 active cases of coronavirus across the country, only five of which are in intensive care, with the death toll at 102.
More than 6500 of the 7109 people diagnosed with the disease have recovered.
Australian Associated Press
