The Health Department confirmed there were no locally acquired cases of Covid-19 recorded in the 24 hours to Tuesday morning, though there were three cases in hotel quarantine.
Some 15,067 Victorians were tested and 9997 received a vaccine dose at a state-run hub during the same period.
Health Minister Martin Foley on Sunday said the state was "on track" to further ease restrictions but warned any changes would be "gradual" and "careful".
He said increased testing would give authorities more confidence the virus wasn't spreading undetected in the community.
Melbourne emerged from a two-week lockdown on Friday, though it was replaced with strict restrictions, including a ban on home gatherings, a 25km travel limit and mandatory masks indoors and out, which will remain until at least June 18.
Regional Victorians are allowed two visitors at home, while density limits are in place at restaurants, pubs and cafes, gyms and other venues.
Residents of a Southbank townhouse complex have been ordered to isolate for up to a fortnight after authorities established a link between two Covid cases who live there.
