Australia was a British colony for more than 100 years, a period during which thousands of Aboriginal Australians were killed and communities were displaced wholesale.
The country gained de facto independence in 1901, but has never become a fully-fledged republic.
In 1999, Australians narrowly voted against removing the queen, amid a row over whether her replacement would be chosen by members of parliament, not the public.
Polls show most Australians are in favour of being a republic, but there is little agreement on how a head of state should be chosen.
The issue was rekindled at the last election, when noted republican Anthony Albanese was elected prime minister. He quickly appointed the country's first "minister of the republic".
"I do support a republic," Albanese told CNN on Sunday, but added that another referendum would have to wait until after a promised referendum on giving Aboriginal Australians an institutional role in policymaking.
"Our priority this term is the recognition of First Nations people in our Constitution," he said.
Thorpe has also called for truth and reconciliation about the past, and a "treaty" that would legally acknowledge Aboriginal historical ownership of the land.