The Liberal senator Andrew Bragg says an Indigenous voice to parliament should be formed by a network of Indigenous communities across the country, in a “bottom-up” approach that would ensure First Nation voices had a direct say to parliament.

Bragg, who has strongly endorsed constitutional recognition, will use a speech in Canberra today to build the case for an Indigenous voice to parliament, outlining a model that he says would honour the Uluru Statement of the Heart, while also upholding parliamentary sovereignty.

Saying he had been “unashamedly vocal” in his support for constitutional recognition, Bragg said consulting Indigenous people on the laws that were relevant to them as proposed by the Uluru statement was both a “good and fair” idea.

He said that ensuring that Indigenous voices were heard by parliament did not mean “creating a third chamber” of parliament, as had been suggested by critics.

In a speech to a Sietar conference on the celebration of Indigenous knowledge on Tuesday, Bragg will propose a voice to parliament that builds on the “Speaking for Country” model put forward in a paper written by the former chair of the government’s Indigenous advisory council Warren Mundine.

“This bottom-up approach involves establishing local and regional bodies for the various Indigenous communities around Australia,” Bragg says.

“It would be for each of these communities to identify a structure that will enable a local or regional body to best represent its community. Indigenous communities around Australia are very different. So their needs are different, and the kind of local or regional body that can help address these needs will be different.”

Once these groups had been formed, the various local and regional bodies would then voluntarily affiliate to create a national body that would facilitate communication between the national parliament and government and the local Indigenous peoples.

“The role of the national body, on this model, will be a bit like a post box or a conduit,” Bragg says.

“It will be the pathway through which the Australian Government and the Australian Parliament are able to speak directly to the local bodies.

“The government and the Parliament will then have a one-stop-shop that they can go to in order to receive advice from Indigenous people.”

Bragg said the “genius” of the proposed model was that the parliament and government would be able to hear directly from the local communities affected by a proposed law or policy.

“In this way, we’ll get a system through which local communities can be heard directly by the Parliament. This is how we’ll get good Indigenous policymaking in Australia.”

In order to provide a “constitutional guarantee” that parliament would hear the voice established through this network, Bragg says the constitution would need to be amended to require the parliament to establish bodies for the various Indigenous peoples across Australia.

But he says a change in the constitution would still give parliament “a free hand” in deciding how they were established.

“So the sovereignty of parliament would be upheld. There would be no third chamber of parliament. And there would be a constitutional obligation for the parliament to set up voices to ensure it can hear the voices of Indigenous people all around the country,” Bragg says.

The detailed proposal being put forward by Bragg comes as the Coalition prepares to announce a “co-design” process for the voice to parliament, for which the government has allocated $7.3m.

After the Indigenous MP Ken Wyatt was appointed as the minister for Indigenous affairs following the May election, he promised to work towards holding a referendum on recognition within three years.

Wyatt has signalled he wants to persist with creating some model of the voice from the Uluru statement, but indicated a representative body might be legislated, rather than enshrined in the constitution, which was the position outlined in the Uluru process.

Conservatives within the Coalition are opposed to a constitutionally enshrined voice to parliament, arguing it could divide Australians on racial grounds.

Bragg said it would be “naïve” to think the issue of constitutional recognition would not provide internal challenges, but said the Liberal party was “used to opening the batting on difficult issues”, pointing to its success on abolishing the White Australia policy, opening trade with Japan in 1957 and delivering the Indigenous referendum of 1967.

“I believe we Liberals are good at big changes because we take the forgotten people or the quiet Australians on the journey,” Bragg said.

“Constitutional recognition is too important to get wrong, and too important to rush.”