Tens of thousands of Australians took to the streets on Friday, protesting a contentious national holiday that also marks the arrival of European colonists more than 200 years ago.

In Sydney, Melbourne and several other cities, thousands of "Invasion Day" protesters demanded the date of the annual Australia Day celebrations be changed.

The public holiday is held on January 26 every year.

For most Australians, it is synonymous with a day off work, a barbecue, Test match cricket, a trip to the beach and the end of the summer holidays.

But the choice of date -- which marks the arrival of European settlers at Sydney Harbour in 1788 -- has become increasingly contentious.

Indigenous activists say Europeans' arrival heralded the start of a centuries-long campaign of cultural genocide.

In a sweltering Sydney, protesters braved 38 degree Celsius (100 Fahrenheit) heat and the ferocious southern sun to wave black, red and yellow Aboriginal flags and chant that the land "always was, always will be" Indigenous.

A banner read "No pride in Australia's genocide".

At a ceremony to grant 16 immigrants citizenship, Prime Minister Anthony Albanese said that Australia Day was "our chance to pause and reflect on everything that we have achieved as a nation".

In a nod to the controversy, he also hailed Indigenous Australians as heirs to "the world's oldest continuous culture" and "the bedrock" of the country's diversity.

"What an extraordinary privilege it is, for their culture to be the beginning of our national story and for their wisdom to be a continuing part of our national life," he said.

On the eve of Australia Day, statues of British colonial figures Captain James Cook and Queen Victoria were damaged in Melbourne.

A statue of the British explorer was felled -- apparently cut off at the shins -- and its plinth sprayed with the words "The colony will fall".

A nearby likeness of British monarch Queen Victoria was daubed with red paint.

Polls show a majority of Australians want to keep the public holiday, but are split roughly 50-50 about changing the date.

Conservative opposition leader Peter Dutton recently denounced a "woke" grocery chain that stopped selling Australia Day branded paraphernalia.

Cricket captain Pat Cummins, perhaps the country's most prominent sports personality, has also weighed in, suggesting a more inclusive date could be found.

"I absolutely love Australia. It is the best country in the world by a mile," he said.

"We should have an Australia Day, but we can probably find a more appropriate day to celebrate it."

Just under four percent of Australia's 26 million people are Indigenous.