Prime Minister Tony Abbott has begun his annual trip to a remote Indigenous community by visiting the gravesite of land rights campaigner Eddie Koiki Mabo on Murray Island in the Torres Strait.

Key points: Abbott is first PM to visit grave of Eddie Koiki Mabo

Abbott is first PM to visit grave of Eddie Koiki Mabo Praised Mabo as a "warrior" who took on legal establishment

Praised Mabo as a "warrior" who took on legal establishment Mabo's campaign overturned terra nullius

Mabo's campaign overturned terra nullius Visit part of PM's week-long tour of remote Indigenous communities

Mr Abbott is the first prime minister to have visited the grave in far north Queensland.

One of Eddie Mabo's daughters Gail took Mr Abbott to the gravesite of her father.

She said her father fought for the acknowledgment of Indigenous rights, a journey that started with the Mabo decision and continues with the push for Indigenous recognition in the constitution.

The Meriam people of Murray Island danced the Malo Kap for Mr Abbott's arrival, a warrior dance reflecting the sacred rituals of the island.

After visiting the gravesite, Mr Abbott said: "This was a warrior, not simply a strong man physically, but a strong man culturally and spiritually, who decided that he would take on the legal establishment".

"He would take on the previously settled view of Australian law, and good on him for having a go, and ultimately good on our system for being able to accommodate Eddie Mabo and the other plaintiffs' cry for justice."

Mr Abbott said Murray Island was "a special place".

"It's a special place, and while this was very contentious two decades back, I think it's now something that has been absolutely accepted by all Australians and a sign of the fundamental justice in Australian society that we not only recognise native title but we appreciate the fact that Indigenous people have rights to their land," he said.

"You only have to look around these communities to see that these people are house proud, to see that people obviously have an enormous amount of self-respect, and this is, I think, something that we should note.

"We all know that there is high levels of dysfunction in some remote places but when it comes to things like sending the kids to school, trying to ensure that there is a strong sense of community spirit and community pride, the people of the Torres Strait really are an exemplar.

"I was lucky enough this morning to go on a run with some local people as part of the Indigenous marathon project and it was terrific to talk to local people who have taken up running.

"It was great for their physical and mental health, great for their self-respect.

Indigenous Affairs Minister Nigel Scullion and Parliamentary Secretary to the Prime Minister Alan Tudge will accompany Mr Abbott for the week, along with secretary of the Department of Prime Minister and Cabinet Michael Thawley.

A string of senior ministers are expected to join him for shorter periods including Attorney-General George Brandis, Health Minister Sussan Ley and Social Services Minister Scott Morrison.

Recognition supported by 'overwhelming majority': PM

Mr Abbott also answered questions about the push to recognise Aboriginal and Torres Strait Islander people in the constitution.

"It's [a] bipartisan policy. I think it's supported by the overwhelming majority of Australians, but we do have to get it right," he said.

Sorry, this video has expired Abbott visits Eddie Mabo's grave on Murray Island

"Obviously there's now a process in place that will be overseen by a referendum council to see if we can come to a reasonable consensus by the middle of next year on what the precise changes might be.

"I am hoping that the referendum council will be announced in the next couple of weeks and I would like to think that within the next couple of months, the community conference process can begin.

"If it's all about Indigenous people in the end, obviously they've got to spend plenty of time thinking about what's right for them, but because our constitution ultimately belongs to everyone, all of the consultations should take place at more or less the same time and under the authority of a referendum council."