Tens of thousands of people have rallied across Australia calling for the abolition of the country's national holiday in protests showing a deep division over a festivity intended to celebrate the birth of modern Australia.

While Australia Day marks the anniversary of the 1788 arrival of the "First Fleet" of British ships at Sydney Cove, many indigenous Australians, who trace their lineage on the continent back 50,000 years, regard it as "Invasion Day".

At a rally in Sydney stretched along more than half a dozen city blocks, about 5,000 protesters chanted, "Always was and always will be aboriginal land" and "No pride in genocide."

Protests attended by several thousand people took place in Melbourne, Canberra and other Australian cities.

Prime Minister Scott Morrison's government, which faces a general election due in May, opposes any change to the holiday.

Attending official celebrations and a citizenship ceremony in Canberra, he said it is idealism and enlightenment, not cruelty and dispossession that have prevailed in the country.

"These great ideas are the foundation of our modern Australia, and they have transformed us into this most recent chapter of our great story - the one we write together," Mr Morrison told crowds in the capital.

Australia's 700,000 or so indigenous people track near the bottom of its 25 million citizens in almost every economic and social indicator.

Divisions have deepened in recent years with increasing calls to change the date.

Amid the heightened sensitivities this week Mr Morrison announced government funding of a voyage to mark the 250th anniversary of explorer Captain James Cook's first journey to Australia.

Canberra pledged about $6.5 million to a circumnavigation of Australia in a replica of Cook's ship, the Endeavour, which in 1770 brought the British into contact with eastern Australia and foreshadowed the colonisation of the continent.

The story of Cook's voyage and his discovery of territory declared New South Wales on the east coast has stirred debate in Australia, with Aboriginal people inhabiting the land for more than 60,000 years before the first European explorers arrived.

Lidia Thorpe, an Aboriginal former member of parliament, was quoted by ABC News as saying that the country never has a time to reflect its first people.

"This country stops for a horse race, it stops for an AFL (Australia Football League) grand final, it stops for the Queen's birthday and it stops for an Anzac service and we don't have ever a time where this country stands still to reflect on first peoples of this country and the pain and suffering we've endured since colonisation".

On Saturday, Indigenous Affairs Minister Nigel Scullion said he was retiring from politics and would not stand in a general election set for May.

"I am grateful that Aboriginal and Torres Strait Islander people have welcomed me in every corner of this continent that I have visited, and worked with me in providing local and national solutions," Mr Scullion said in a statement posted on his website.