Several thousand people rallied in Melbourne against new vaccination mandates on Saturday, with a few comparing the state government to Nazis and calling for violence against politicians, local media said.

In Australia, where 83% of people aged 16 and above have been fully inoculated against the coronavirus, nationwide vaccinations are voluntary. But states and territories have mandated vaccinations for many occupations and barred the unvaccinated from activities such as dining out and concerts.

The Melbourne demonstration against the vaccination mandate that came into effect on Saturday - requiring construction workers in Victoria state to be fully inoculated - was peaceful, with no immediate reports of unruly behaviour or arrests.

But a reporter at The Age posted video on Twitter of a protester carrying a mock gallows with three nooses hanging from it, and the newspaper showed a protester carrying a poster depicting Victorian Premier Daniel Andrews with a Hitler moustache and the hashtag #DictatorDan.

"We're being governed by insane medical bureaucrats," Craig Kelly, former Liberal Party member of parliament and now the leader of United Australia Party, told the rally, media reported.

The Age said some protesters called for violence against politicians but did not offer specifics.

An Australian singer Claire Woodley dedicated a song to "victims of satanic ritual abuse" - a rhetoric common in the QAnon conspiracy theory about abducting children for satanic rites.

Andrews' office and protest organisers could not immediately be reached for comment.

Australia has seen frequent, occasionally violent, anti-vaccine rallies in recent months, though the movement remains small, with polls showing nationwide opposition in the single digits.

Victoria, the second-most populous state with a quarter of Australia's 25 million people, has an 87% vaccination rate and has endured six COVID-19 lockdowns totalling nearly nine months.

There were 1,221 new infections reported on Saturday in Victoria and four deaths, and 250 daily cases in New South Wales.

Despite Delta outbreaks that led to months of lockdown in the two largest cities, Sydney and Melbourne, the national tally of just under 190,000 infections and 1,591 deaths is far lower than that of many developed nations.

Neighbouring New Zealand, which is also learning to live with the coronavirus through high vaccination rates, reported 175 new cases, bringing the total number of confirmed cases since the start of the pandemic to 8,121. There have been 33 deaths in total.

In major cities across New Zealand, several anti-government protests against COVID-19 measures took place, with people driving slowly on main roads to cause traffic congestion.

"Crass and stupid but what else would you expect!" Auckland Mayor Phil Goff said in a message on his Facebook page.