Victoria has recorded one new locally-acquired case of coronavirus.
The health department on Sunday confirmed the new case is a close contact of an already infected person.
They have been quarantining throughout their infectious period.
Some 17,102 Victorians were tested in the 24 hours to Sunday morning, while 14,390 received a COVID-19 vaccine dose at state-run hubs.
It comes as authorities work to link Saturday's local virus case to the Kappa strain outbreak.
The case, a man living in central Melbourne with his young family, is a "mystery case" until a connection is found.
Testing commander Jeroen Weimar said he was confident this link would be found but said he was more concerned about undiscovered cases because of low testing rates.
"There may well be more out there," he told reporters on Saturday.
He asked Victorians to make each other accountable for possible coronavirus symptoms and to encourage each other to get tested.
"Call them out in the nicest possible way," he said.
Following a two-week lockdown that ended on Friday, Melburnians are allowed to travel up to 25km from home and meet outside in groups of up to 10. Masks are required indoors and outdoors and hospitality, retail and schools have reopened.
There are more than 3000 primary close contacts in quarantine as a result of community cases, as well as 122 exposure sites listed on coronavirus.vic.gov.au.
Health Minister Martin Foley would not make any commitment to the further easing of restrictions in Melbourne, slated for Thursday.
He implored Victorians to obey restrictions, sign in with their smart phone at all venues with a QR code, get vaccinated as soon as eligible and get tested for virus with the slightest of symptoms.
Opposition health spokesperson Georgie Crozier criticised the government for lacking a plan for the path out of restrictions, asking how many daily tests would make them confident.
Meanwhile, Prime Minister Scott Morrison is in the UK taking part in talks on a more equal global distribution of vaccinations and how to best prepare for outbreaks of other diseases.
While a thorough probe into the origins of the coronavirus is necessary to avoid a repeat in future the aim is not to pin blame on anyone, Mr Morrison said.
The Australian government's strong support on the international stage for an investigation into how COVID-19 emerged has angered officials in Beijing and further damaged strained relations with China, where the World Health Organisation says the virus was first detected in late 2019.
"The purpose of these inquiries is to understand - it's got nothing to do with politics or frankly blame or anything else - it is about understanding it," Mr Morrison said.
"So we all, on a future occasion should it occur, can move quickly and can respond and avoid ... the absolute carnage that we've seen from this pandemic to both lives and livelihoods all around the world."
