Two historic statues were damaged in Melbourne ahead of Australia Day celebrations where tens of thousands across the country have joined protests in support of Aboriginal people who say the date is not one to celebrate.

A statue of colonist John Batman, a founder of the country's second largest city who was also involved in killings of Indigenous people, was sawn in half, while a monument commemorating Australian soldiers in World War One was daubed in red paint, with the words "land back," in the early hours of Saturday morning, local media reported.

Australia's national day on January 26 is a controversial date for Indigenous Australians because it marks the date that Britain established the state of New South Wales in the east as a penal colony in 1788, and the beginning of the country's colonisation by the British.

Thousands of people gathered around Australia to protest. - AP

For many Indigenous Australians, who trace their lineage on the continent back 50,000 years and make up about 4 per cent of the country's population of 27 million, the Australia Day holiday is known as Invasion Day, symbolising the destruction of their cultures by European settlers.

In Sydney, the artwork of Wiradjuri-Biripi artist James P. Simon was projected on to the sails of the Opera House, as part of many dawn ceremonies around the country to be followed by protests and festivities throughout the day.

In Melbourne, tens of thousands lined the steps of state parliament, in what organisers described as the biggest turnout to date, to demand justice for Indigenous deaths in custody and missing and murdered women, and holding governments to account in treaty negotiations.

Chants of "shame", "long live the resistance" and "from the river to the sea, always was always will be" rang out throughout the crowd as a dozen speakers addressed the crowd.

The sails of the Sydney Opera House on January 26. – AAP

Victoria Police said they had done "extensive planning" for Australia Day events and rallies while NSW Police promised to use "proactive policing strategies" to ensure minimal impact on the community.

Meanwhile Australians, young and old, indigenous and those about to become citizens gathered in Canberra to celebrate the country's national day.

Prime Minister Anthony Albanese said during the ceremony which included flag raising and citizenship ceremonies, performances by indigenous dancers, as well as a 21-gun salute.

"From the unique privilege that we have of sharing this oldest continent with the world's oldest, continuous culture. To the multicultural society we've built, where everyone has the right to be proud of who they are, to worship how they choose and to live in peace and safety, side by side,” Albanese said. 

In Melbourne, a smaller unrelated pro-Australia Day rally is planned outside Melbourne Park which is the home of the Australian Open, however it's not expected to cross over with other rallies and police say organisers have provided them with details about their plans.

Music lovers will descend on Sydney Harbour for the Australia Day Live concert set against the backdrop of the Opera House, while other free concerts are being held around the nation.

Heatwave warnings have been issued across the nation, with alerts current for much of Queensland, northern NSW, parts of South Australia, central Western Australia and southern parts of the Northern Territory.

The Bureau of Meteorology said severe heatwaves can be dangerous for many people including older people, babies, children, pregnant and breastfeeding women and those with medical conditions.

"Seek a place to keep cool, such as your home, a library, community centre or shopping centre," the bureau said.