But Finance Minister Jim Flaherty will be conspicuous by his absence.
Forging a new fiscal relationship is central to the meeting, with both aboriginal leaders and the government alike recognizing a pressing need to discuss how money is best spent.
Actual money won't come until the next federal budget at the earliest.
"It's not a budget negotiation. It's much more than that," National Chief Shawn Atleo said in an interview Friday.
First Nations leaders want an end to the unpredictable nature of the current grant-based funding — a system that has frequently been criticized by the federal auditor general for being unreliable and preventing solid planning.
Instead, they want a new framework that would see a statutory commitment to continuing funding that would see the responsibility shared by both the federal government and First Nations leaders.
"It's about completely transforming the way we do our work. And it's about seeking commitments that the Crown will work with us to change the fiscal relationship, that we would move towards more stable, long-term fiscal relationships," Atleo said.
"And that we would do that work together, and that we would move away from the unilateral nature of decision making."
Flaherty's sanction is not really necessary for those kinds of conversations. But for First Nations, changing the fiscal structure is only the first step.
Follow-up in the next budget is crucial, especially on education, if the federal government is going to live up to its commitments under the United Nations Declaration on the Rights of Indigenous Peoples signed recently by Canada, First Nations leaders say.
"I would certainly be looking to the upcoming budget," Atleo signalled.
The start of the next fiscal year will be the sign for many First Nations about whether Stephen Harper is serious about working with aboriginals, says Grand Chief David Harper of the Northern Manitoba Chiefs.
At that point, native communities will feel the practical impacts of improvements Harper has committed to, or whether he plans to cut funds for housing — as many chiefs suspect.
"The results, they'll say a lot," Chief Harper said in a telephone interview.
At a minimum, chiefs want to see parity with non-First Nations people on funding for education, child welfare and social services. But those items alone would cost the federal government billions of dollars.
Atleo does not expect to see any dollars Tuesday, but he says he believes the government does have serious intentions of making fundamental changes to its relationship with First Nations.
The fact that the prime minister is bringing such a large contingent of ministers shows he is dedicating the "full machinery of government" to the talks, Atleo said.
"I receive that as a positive sign."
Prime Minister Harper has stated that he favours an "incremental" approach to the summit — one that favours setting out a plan of gradual steps, rather than a grandiose announcement.
Atleo, by contrast, has spoken of wanting to "smash the status quo." And he is under intense pressure from First Nations across the country to show that the first such meeting in years can produce solid results.
"We can be both practical and ambitious," Atleo said in the interview.
The meeting with the prime minister and cabinet ministers should serve to recognize key principles: that First Nations all have a treaty relationship with the federal government, and that those treaties include specific rights that need to be recognized.
But the meeting also needs to include concrete steps, such as setting up a task force on economic development, Atleo added.
That group would have to come to grips with treaty rights that are supposed to grant First Nations a share of the revenue from natural resources, Atleo says.
Revenue sharing has always been a non-starter with the federal government, but for First Nations, it's key to prosperity and independence.
There's no need for government hand-outs if First Nations have access to some of the proceeds that come from their lands, said Chief Harper.
And the meeting also needs to include more than just statements of principle about the importance of education, added Roberta Jamieson, chief executive of the National Aboriginal Achievement Foundation and a widely respected leader.
"I am weary of process for process' sake," she said in an interview.
She wants a new structure, piloted by a new unit in the Prime Minister's Office, that would commit to equitable funding from kindergarten to post-secondary levels of education.
"This shouldn't be a one-meeting wonder," she said.
Atleo couldn't agree more. With just two hours to spend in dialogue with the prime minister next week, he wants to see an annual commitment to revisit the commitments and set out next steps.
"We should check back in a year."