Australia's Victoria state reported five new local COVID-19 cases on Saturday amid a strict lockdown, as people rushed to vaccination centres, causing long lines and technological glitches.

The infections bring the latest cluster to 35, but the number of exposure sites visited by the infected people has expanded to more than 150, putting thousands at risk.

Victoria entered into the weeklong lockdown on Thursday night, the state's fourth in the pandemic, forcing residents to remain at home.

"We are taking this outbreak day by day," Victoria's commander of COVID-19 response, Jeroen Weimar, told a news briefing. "It is day two of a seven-day lockdown. We asked for seven days because there is a lot of work depth to go into."

The outbreak was caused by a traveller who left hotel quarantine in South Australia state after testing negative but later tested positive in Melbourne.

People lined up for several hours at vaccination centres on Saturday, trying to book a shot or get one on a walk-in basis. A designated state hotline for booking has crashed continually since Thursday.

"We have seen a record people coming forward, so my message is, do not give up, we are doing everything we possibly can," Victoria's Health Minister Martin Foley told the briefing.

Getting a coronavirus vaccination is one of the five reasons for which Victorians may leave their houses. The others are essential work, healthcare, grocery shopping and exercise. Shopping and exercise are limited to two hours per day.

Australia has effectively contained all past outbreaks through speedy contact tracing, snap lockdowns and strict regional border controls, helping keep its COVID-19 numbers relatively low, with just over 30,070 cases and 910 deaths.