Chief Theresa Spence of the remote Attawapiskat First Nation launched her protest with a vow to "die" unless the Conservative government starts showing more respect to First Nations concerns and aboriginal treaties.
Spence wants the Crown, Prime Minister Stephen Harper and aboriginal leaders to work together to forge a new relationship.
An offer was extended last week to have Duncan's parliamentary secretary visit Attawapiskat to ensure the reserve has what it needs to get through the winter, said Jan O'Driscoll, a spokesman for the minister.
"We continue to look forward to her response," O'Driscoll said.
Duncan would also be prepared to meet Spence this week in Ottawa to discuss the state of her community, he added.
But the issues go well beyond Attawapiskat, Spence said in a statement.
The Harper government has embarked on an "aggressive, assimilatory legislative agenda" that flies in the face of the United Nations declaration on the rights of indigenous peoples, she complained.
And she accused Duncan's office of misleading the public about the social realities facing Canada's First Nations.
Spence was at the centre of an international media storm last year because of a winter housing crisis in her remote community.
She says she wants the federal government to withdraw recent legislation which she claims was forced on aboriginals. She also wants it to reverse its decision to cut funding to First Nation organizations and communities.
Thousands of protesters in cities across the country took to the streets Monday in what has been dubbed the Idle No More movement against what they say are unilateral actions by the Harper government.
They are angry over a number of bills before Parliament, including one that would force First Nations to disclose their financial statements and the salaries of chiefs and councillors.
They are particularly upset with Bill C-45, the government's omnibus budget legislation, which they say weakens environmental laws.
For Spence, the pain of watching her people suffer through a lack of housing and inadequate water supplies proved a tipping point.
"The treaty's been violated (for) so many years and it’s time for the prime minister to honour it and respect our leaders,” said Spence, who is staying in a cabin on an island in the Ottawa River while she goes without food.
"I am willing to die for my people because the pain is too much and it’s time for the government to realize what it’s doing to us,” she said.
"I am not afraid to die. If that’s the journey for me to go, then I will go."
One post on social media websites set up by the Idle No More organizers accuses Prime Minister Stephen Harper of abandoning aboriginal people.
"A few Canadians get E. coli sickness and Harper shuts down XL Foods," reads the post, referring to the recent closure of an Alberta meat processing plant over a contamination scare.
"But Cree are dying in (Fort Chipewyan, Alta.) from toxins in their water, yet Harper keeps the tar sands open."
The government has said it holds thousands of consultations with aboriginal leaders every year and that Duncan has personally visited dozens of reserves over the last two years.
And it says it's still waiting for a strategy from Attawapiskat to deal with the community's housing shortage.
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