Health Minister Martin Foley confirmed two residents of the Kings Park Apartment Complex at Southbank tested positive on Tuesday, though they will be included in Wednesday's official figures.

The two new cases, adult men who live in separate apartments, were among more than 200 residents tested on Monday after authorities established a link between two other cases who live there.

Authorities believe transmission between the two cases occurred in a common area of the complex.

Six residents have now tested positive for COVID-19.

Three were transferred to hotel quarantine upon testing positive, while a newborn baby remains in an apartment with its mother.

COVID-19 Commander Jeroen Weimar said the men lived in apartments adjacent to those occupied by positive cases.

"Those two positive cases are connected to some communal areas that we are concerned about, thoroughfares within that particular complex," he told reporters.

The low-rise complex, which consists of about 100 townhouses, has now been listed as a Tier 1 exposure site from June 2 to June 14.

As a result, all residents in the building have been asked to self-isolate for the next 14 days.

Mr Wiemar said authorities would provide residents with all necessary support to get through the coming days.

"It's a very challenging thing to be asked to isolate for 14 days when you weren't expecting it," he said.

"But it's so important as we finally get to what we think and what we hope are the last vestiges of these outbreaks that we really close and corner it and make sure we address any other residual risks that we have in greater Melbourne."

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.

Mr Foley said further easing of restrictions remained a "day-by-day proposition".

Earlier, the Health Department confirmed there were no locally acquired cases of COVID-19 recorded in the 24 hours to Tuesday morning, while 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.

Active cases in the state dropped from 64 on Monday to 54 on Tuesday.

Meanwhile, walk-in vaccinations for the Pfizer vaccine at state-run hubs have been halted for the rest of the week, in an attempt to preserve supply for already booked first and second doses.

Amid the latest outbreak, the state's vaccine rollout was expanded to all Victorians aged 40 and over, leading to a surge in demand that has outstripped supply.

"Anyone due a second dose will be getting a second dose, but we can't keep doing the first doses at the rate that we would like to - and the rate at which Victorian show they have an appetite for - because we simply won't have enough vaccine for future provision," Mr Foley said.

Australian Associated Press