Marking Australia Day is like celebrating the Holocaust, a Melbourne politician said as her council scrapped a holiday it deemed offensive to Aboriginal people, in a move the government on Thursday labelled 'extreme and divisive'.

The council in the Melbourne suburb of Moreland became the third in Victoria state to decide not to recognise Australia Day.

The annual holiday, on January 26, commemorates the arrival of the country's first British settlers in 1788 and is a time when citizenship ceremonies are held.

Australia's colonial history credits Captain James Cook with discovering the country, but Aboriginal people inhabited the land for more than 60,000 years before the first European explorers arrived

But it is termed 'Invasion Day' by many indigenous Australians who say it marks the beginning of the decline of Aboriginal culture.

In debating the issue Wednesday, Moreland Socialist Alliance councillor Sue Bolton said commemorating Australia Day 'would be like celebrating the Nazi Holocaust', state broadcaster ABC reported.

Assistant Minister for Immigration Alex Hawke said in a statement the government rejected 'the extreme and divisive nature of the discussion Greens and Socialist councillors are promoting'.

He said the government of Prime Minister Malcolm Turnbull 'strongly condemns comparisons of Australia Day with the Nazi Holocaust as deeply offensive to all Australians'.

'Australia Day is a recognition of our shared history and the Turnbull government, along with the vast majority of Australians, indigenous and non-indigenous, fully support Australia Day remaining on January 26.'

Koomurri people and representatives of Aboriginal groups from around Australia perform the Smoking Ceremony and Dance as part of an Australia Day ceremony in Sydney, in January

Australia's colonial history credits Captain James Cook with discovering the country, but Aboriginal people inhabited the land for more than 60,000 years before the first European explorers arrived.

Last month a war of words erupted over colonial-era statues in Australia, with several in Sydney defaced, including one of Cook with the words 'change the date' in reference to Australia Day.

The vandalism sparked a furious response from Turnbull, who brushed off calls for the statues to be torn down, adding that the defacement was 'what Stalin did' in denying history.

Aborigines remain the most disadvantaged Australians. They were believed to have numbered around one million at the time of British settlement, but now make up only about three percent of the total population of 24 million.