Political leaders should keep an "open mind" to calls from Indigenous leaders for a new representative body, Federal Opposition Leader Bill Shorten says.

Key points: Shorten vows Labor will not shy away from "big questions"

Shorten vows Labor will not shy away from "big questions" Turnbull warns constitutional change would be "very difficult"

Turnbull warns constitutional change would be "very difficult" Dodson says constitutional recognition still open for discussion

After three days of talks in central Australia, Indigenous leaders on Friday released the Uluru statement, rejecting "simple acknowledgement" of Indigenous people in the constitution.

They have instead called for a representative body to be enshrined in the nation's founding document, and for a process to be established to work towards treaties between governments and Indigenous Australians.

Mr Shorten did not commit the Opposition to those ideas, but he used a speech at a lunch celebrating the 1967 Indigenous referendum to vow Labor would not shy away from "big questions".

"We owe the [Uluru delegates] an open mind on the big questions. On the form recognition takes, on treaties, on changes required in the constitution," Mr Shorten said.

"And on the best way to fulfil the legitimate and long-held aspiration of Aboriginal people for a meaningful, equal place in our democratic system."

PM cautious of challenges

Prime Minister Malcolm Turnbull spoke at the same event, but was more circumspect than Mr Shorten.

Mr Turnbull repeated his warning that constitutional change would be "very difficult".

"History would indicate that to succeed, not only must there be overwhelming support, but minimal — or at least tepid — opposition," Mr Turnbull said.

Mr Turnbull said the referendum council and then the Parliament would consider the recommendations made at Uluru.

But he did not directly mention any of the specific demands in the Uluru statement, and said the challenges of constitutional change should not be underestimated.

"The constitution cannot be changed by Parliament. Only the Australian people can do that. No political deal, no cross-party compromise, no leader's handshake, can deliver constitutional change," he said.

"To do that, a constitutionally conservative nation must be persuaded that the proposed amendments respect the fundamental values of the constitution, and will deliver precise changes, clearly understood, that benefit all Australians."

Some Government backbenchers have previously warned that only "minimalist" changes to the constitution would win support in the Coalition party room and the broader community.

Coalition frontbencher Simon Birmingham said the Coalition wanted to ensure that the push for constitutional change was successful.

"There are risks to be weighed, and we will weigh them properly. We want to make sure due consideration is given in a respectful manner to these recommendations," Senator Birmingham said.

"But of course if we are to proceed with constitutional recognition of Indigenous Australians, we need to make sure we proceed in a way that gives it the best chance of success, the best chance of being unifying."

Constitutional recognition still open for discussion: Dodson

Earlier, Aboriginal leader and federal Labor frontbencher Pat Dodson cautioned the Government not to "abandon" the work it had already done on constitutional recognition in the wake of the Uluru statement.

Senator Dodson says treaties could be enacted without constitutional change. ( ABC Goldfields-Esperance: Jarrod Lucas )

"It's fine there's come this report out of Uluru, talking about an entrenched voice into the constitution, that will have to be weighed and considered, but I don't think we should just dismiss out of hand the work that was done by the expert panel [on constitutional recognition]," he said.

"I think in the finer print of what's come from Uluru, there seems to be … still room to have discussions about those matters."

Before entering Parliament, Senator Dodson chaired the expert panel which handed its findings to the Gillard government in 2012.

It recommended repealing two sections of the constitution which allow governments to make laws applying only to certain racial groups.

The panel also said those sections should be replaced with sections acknowledging the "continuing relationship" of Aboriginal and Torres Strait Islander peoples with their traditional lands, and the need to secure their advancement.

A parliamentary committee made similar recommendations in 2012.

The Greens have already thrown their weight behind the Uluru statement.

"Now more than ever it is vital that the Government acts on its rhetoric with sincerity and start the process outlined in the statement," Greens senator Rachel Siewert said.

"It is the powerful position by the first peoples of this country and cannot be ignored."