"So far, data has been accessed fewer than 10 times."
On Wednesday, Victoria's Chief Health Officer Brett Sutton told reporters "there haven't been new contacts identified through the use of the COVID-19 app".
SBS News contacted Victoria's Department of Health and Human Services to enquire if this had changed since but was not provided with the information.
"We urge Victorians to download the app to enhance our contact tracing tools to stop the spread of the virus. This will be increasingly important as restrictions are eased further and people are more mobile," a spokesperson said.
No other state or territory has reported finding an unknown close contact through the COVIDSafe app.
More than six million Australians have downloaded the app.
Launching the app in April, Mr Morrison said it was vitally important to Australia's recovery.
"We need the COVIDSafe app as part of the plan to save lives and save livelihoods," he said.
"The more people who download this important public health app, the safer they and their family will be."
On Saturday, Centre Alliance senator Rex Patrick said the government was refusing to concede the app "wasn't working properly, if at all".
"I think the prime minister and the government were dishonest with the Australian public and I think that that's very sad," he told the Sydney Morning Herald and the Age.
Federal government COVID-19 material continues to stress the benefits of the app.
"COVIDSafe is one of the tools we'll use to help protect the health of the community by quickly alerting people who may be at risk of having contact with the virus," Department of Health material says.
"Use of COVIDSafe will allow us to lift restrictions earlier than would otherwise be possible."
It comes as the government has denied it is about to permanently lift the dole payment JobSeeker, which replaces the Newstart allowance.
News Corp newspapers, citing senior ministers, had reported the JobSeeker payment would rise to $75 per day from $40 when the present enhanced version of the unemployment payment ends in September.
"There are no such proposals before the government or under consideration for the economic statement next month," a spokesperson for Social Services Minister Anne Ruston said on Sunday.
"The government is focused on the next phase of short-term measures designed to address the COVID-19 crisis."
The JobSeeker payment was doubled to around $1,100 a fortnight as a support measure during the pandemic.
Treasury has been reviewing both JobSeeker and the JobKeeper wage subsidy.
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Senior Labor frontbencher Tanya Plibersek said people who had been forced on to the dole because of the coronavirus pandemic were in for a shock if the JobSeeker payment returned to its pre-crisis rate of $40 per a day.
"It is an inadequate payment, it doesn't allow people to live with dignity," she told Sky News' Sunday Agenda program.
"We now have hundreds of thousands of extra people joining the dole queue, people who have been working full time until very recently that would very much struggle if what's now called JobSeeker went back to the old Newstart rate."
The coalition government has long argued against raising the unemployment payment, which hasn't been increased for 25 years apart from indexation increases.
There is widespread support for an increase from Labor, the Greens, welfare groups, business organisations like the Business Council of Australia and the Australian Industry Group, economists and the Reserve Bank.
Additional reporting: AAP
People in Australia must stay at least 1.5 metres away from others. Check your state’s restrictions on gathering limits.
Testing for coronavirus is now widely available across Australia. If you are experiencing cold or flu symptoms, arrange a test by calling your doctor or contact the Coronavirus Health Information Hotline on 1800 020 080.
The federal government's coronavirus tracing app COVIDSafe is available for download from your phone's app store.
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