The prime minister argues that is exactly why Australia Day should be held on the date each year.

"We do it on this day when the course of this land changed forever," he said in Canberra on Tuesday.

"There is no escaping or cancelling that fact, for better or worse."

Mr Morrison said January 26, the day Captain Arthur Phillip raised the Union Jack and proclaimed British sovereignty in 1788, marked the beginning of modern Australia.

"Our stories since that day have been of sorrow and of joy, of loss and redemption, of failure and of success," he said.

"We are now a nation of more than 25 million stories. All important, all unique, and all to be respected."

British colonisation led to widespread massacres, oppression and dispossession of Indigenous people from land they had inhabited for more than 60,000 years.

The prime minister delivered the keynote address at a flag-raising and citizenship ceremony on the shores of Lake Burley Griffin, attended by the governor-general and other dignitaries.

A C-130 Hercules transport plane pierced the clouds and an enormous flag was suspended from an Army helicopter, before 25 new citizens made their pledge to Australia.

More than 1000 people marched from the Tent Embassy to Parliament House for Canberra's Invasion Day rally.

Melbourne's demonstration went ahead despite the city's annual Australia Day parade being called off.

In Sydney, protesters defied demands to stay away, but were wary of warnings they could face fines or prison time for breaching coronavirus health orders.

Conservative lobby group Advance Australia paid for the letters "Aus Day" to be written in the sky above Sydney on Tuesday, to counter the Invasion Day rally.

Australia Day in Sydney began at dawn with the Sydney Opera House sails lit with Indigenous art.

Shortly after first light, the Aboriginal flag was raised alongside the Australian flag on the Sydney Harbour Bridge.

Similar early morning ceremonies were held across the country.

Australian Associated Press