"The more Australians who take this up the more secure we are about our public health response."
Dr Murphy has predicted more than 50 per cent of Australians will take up the app.
The government has said 40 per cent - or some 10 million people - would be needed for contact-tracing to be most successful.
Dr Murphy also defended the 15 minute time limit for the app to record interactions between users, amid concerns from some it would not record shorter meetings.
"You wouldn't want to be capturing every brief contact," he said.
"We don't want to give the contact tracers a list of 1000 phone numbers when there are 25 that are much more relevant in terms of potential contact."
He said this decision was made on the best epidemiological advice of the interactions most at risk of passing on the virus.
Data protection groups have called on the government to release the source code for the app - essentially its blueprint - for independent analysis.
The health department's chief information officer Daniel Keys said the code would "absolutely" be released.
"We will release the source code for everything that's safe to do so," he said.
"That's being addressed by the Australian Cybersecurity Centre and then we will make it available. We will release it within two weeks."
Earlier, Health Minister Greg Hunt also welcomed the public's initial uptake of the app.
"We had hoped that perhaps we would get to the million mark within five days and we were lucky to get there within five hours," Mr Hunt said.
"Australians, just as they have done throughout the course of the virus, have responded magnificently and it is a simple thing."
Called COVIDSafe, the voluntary app has been backed by doctors, nursing, business and banking groups.
On Sunday, Mr Hunt said anyone concerned about privacy could use a fake name when they registered for the app.
"Yes you can - that's legally available," he said.
The Australian app is based on Singapore's Tracetogether software, which records the Bluetooth connections a phone makes with others so the user can give that data to state health authorities if they catch the virus.
While launching the app on Sunday, Mr Hunt said it will "save lives and protect lives".
"It is about assisting and finding those cases which may be undiagnosed in the community, helping people get early treatment, have early diagnosis and to ensure that our doctors and nurses, our health workers, our families and friends are protected," he said.
The government hopes a broader testing regime and the contact tracing app will lead to a relaxation of the economic shutdown sooner.
Prime Minister Scott Morrison told the ABC that only health authorities would have access to the data.
"It's another tool we need to get back to normal as much as we can," he said.
He said the contact numbers picked up by a person's phone are only downloaded by a health officer when someone gets the coronavirus and gives permission.
"No other government agency can use this information, no one in the commonwealth government at all, and in state authorities, only the health officer can use it," he said.
"Not the police, not the welfare people, nowhere else. Just the health officer."
Labor health spokesman Chris Bowen said the app had been activated under the Biosecurity Act as an interim measure, but expects it will be legislated when parliament sits in mid-May and that will be important to assure Australians of their privacy.
"I'd be happy to download the app," Mr Bowen told reporters in Sydney.
"The only people I've seen say that they won't download the app are Liberal and National MPs."
Australian Medical Association President Tony Bartone told reporters the app was an important part of Australia's response to the pandemic.
"The COVID-19 COVIDSafe app will assist in the contact tracing process, that laborious slow process which, together with the marvellous community response, has been implicitly responsible for reducing the spread of COVID-19 in the community and flattening the curve," Dr Bartone said.
Business Council of Australia chief executive Jennifer Westacott urged all Australians to download the app.
"The more Australians who download the app the safer we will all be and the more quickly we can begin to ease restrictions," she said in a statement.
Australian Nobel laureate and immunologist Peter Doherty said he would be signing up for it.
"Anything that helps us wrestle COVID-19 to the ground is a plus. Any privacy any of us had pretty much disappeared when we started using mobile phones, searching online, buying stuff from Amazon or whatever," he tweeted on Sunday.
New research from the Australia Institute shows that 45 per cent of Australians say they will download and use the mobile app, while 28 per cent say they won't. A further 27 per cent were unsure.
People in Australia must stay at least 1.5 metres away from others and gatherings are limited to two people unless you are with your family or household.
If you believe you may have contracted the virus, call your doctor (don’t visit) or contact the national Coronavirus Health Information Hotline on 1800 020 080. If you are struggling to breathe or experiencing a medical emergency, call 000.
SBS is committed to informing Australia’s diverse communities about the latest COVID-19 developments. News and information is available in 63 languages at sbs.com.au/coronavirus.
Additional reporting by Evan Young.