Professor Murphy on Sunday said there was nowhere else he would rather be than Australia at the moment, but people in the community are still transmitting Covid-19.
"That is why we have to keep our pressure on and make sure that we don't end up like countries in the world that you have all seen on the news," he told reporters in Canberra.
"We are in a good place ... but we have to maintain that good place".
There were 6313 confirmed Covid-19 cases in Australia as of Sunday afternoon.
The death toll rose by three to 59 with the death of a 74-year-old man in hospital in South Australia after contracting the virus on the Ruby Princess cruise ship, the death of a woman in her 70s in Tasmania and the death of an 82-year-old man in Sydney.
Federal treasurer Josh Frydenberg warned it would be "very dangerous and unrealistic" to remove social distancing restrictions too soon.
He said they would stay in place "for as long as it takes".
"We have got to take the medical advice," Mr Frydenberg told the ABC.
The Tasmanian government on Sunday closed two hospitals at the centre of a coronavirus outbreak involving 49 cases in the state's northwest.
All hospital staff and their households, more than 1000 people, will be placed into quarantine for two weeks as a "super clean" of the facilities is undertaken.
South Australia reported good news, with no new virus cases recorded for the first time in more than a month.
In Victoria, Premier Daniel Andrews announced the state of emergency imposed in his state was being extended by four weeks to midnight on May 11.
Meanwhile, the government launched emergency contingency measures to ensure aged care recipients continue to get the care they need during the pandemic.
The measures include new emergency response teams on standby if there's a significant outbreak in a residential aged care facility.
There will also be remote locums to support aged care providers in remote Australia if they are unable to source staff.
