Britain's King Charles was embraced by an Indigenous elder after a welcome smoking ceremony on Tuesday in the birthplace of Australia's urban Aboriginal civil rights movement in Sydney, a day after being heckled by an Indigenous senator in Canberra.

Charles met with Indigenous elders at the National Centre for Indigenous Excellence in inner-city Redfern, including "bush tucker" - or native food - chef Aunty Beryl Van-Oploo, who served kangaroo pies.

The king was embraced by elder Michael Welsh, and a woman introduced herself as a member of the Stolen Generation - a reference to Aboriginal children systematically removed from their families decades earlier. "Welcome to this country," she said.

A day earlier, Charles was heckled at Parliament House in Canberra by independent senator and Indigenous activist Lidia Thorpe who shouted that she did not accept his sovereignty over Australia, and demanded a treaty for Indigenous people.

While the atmosphere at Redfern on Tuesday was respectful, some people who came to see the king expressed sympathy for Thorpe's actions.

"We've got stories to tell and I think you witnessed that story yesterday," Metropolitan Local Aboriginal Land Council Chairperson Allan Murray said.

In a radio interview with the Australian Broadcasting Corporation on Tuesday, Thorpe said she "wanted the world to know the plight of our people".

Former Olympic athlete Nova Peris, who was the first Indigenous woman elected to federal parliament, wrote in a social media post she was "deeply disappointed" by Thorpe's actions, which "do not reflect the manners, or approach to reconciliation, of Aboriginal Australians at large".

Emotions around Indigenous rights and Australia's colonial history are raw after a national referendum on whether to alter Australia's constitution to recognize Aboriginal people was rejected last year.

Charles referred to Australia's "long and sometimes difficult journey towards reconciliation" in a speech on Monday before he was heckled by Thorpe.

Under glorious spring skies, the king later visited a social housing project designed with the support of his King's Trust Australia charity in the inner suburb of Glebe.

He toured the construction site with Prime Minister Anthony Albanese, who grew up on a public housing estate, and met Indigenous actor Wes Patten, one of three apprentice construction workers on the project.

Patten played the son of an Indigenous politician in TV political drama "Total Control", depicting the imagined first Indigenous prime minister of Australia.

Claude Tighe, an Indigenous man in Glebe who saw the Lidia Thorpe protest on social media, said: "I want him to talk to real traditional owners. There’s a lot of us here".

“She spoke for Aboriginal people,” he added, referring to Thorpe.

In the afternoon, Charles visited a skin cancer clinic where he met cancer survivors and researchers working on cures for the disease.

The visit to the Melanoma Institute Australia was one of the final public appearances Charles made on his 16th official visit to the country, his first major overseas trip since being diagnosed with an unspecified form of cancer.

There was no mention of his own diagnosis during the visit, where Charles met melanoma survivor Adam Brown and his family. Brown was given 12 months to live when he was diagnosed in 2015.

Brown, along with wife Kristy, introduced their children as their “two miracles”.

The king offered his congratulations to Brown although jokingly wondered why the children were meeting him during school hours.

Charles also met renowned melanoma researcher and brain cancer survivor Richard Scolyer. Diagnosed with brain cancer last year, Scolyer underwent world-first surgery and his tumor is in remission.

Scolyer was joined on Tuesday by fellow researcher Georgina Long. Both were named Australians of the Year in January for their research into melanomas.

"That was an amazing opportunity for us to tell the king about what we're doing here trying to deal with Australia's national cancer, and to talk about how we're trying to get to zero deaths from melanoma," Scolyer said,