Describing Canada as a "work in progress," Prime Minister Justin Trudeau told the UN Thursday about the country's failures and mistakes in its historical relationship with Indigenous people and his hope to right the wrongs of the past.

"There are, today, children living on reserves in Canada who cannot safely drink, or bathe in, or even play in the water that comes out of their taps," Trudeau said in a speech to the UN General Assembly.

He said Indigenous families putting their kids to bed at night are beset by worry that their children will run away before morning or commit suicide in the night.

"And for far too many Indigenous women, life in Canada includes threats of violence so frequent and severe that Amnesty International has called it 'a human rights crisis,'" Trudeau said.

The prime minister said his government was working with Indigenous leaders to improve the situation and address gender-based violence as well the lack of safe drinking water and affordable housing on reserves.

"We need women and girls to succeed, because that's how we grow stronger economies and build stronger communities," Trudeau said. "That is why our government will be moving forward shortly with legislation to ensure equal pay for work of equal value."

Trudeau said improving the daily life of Canada's Indigenous people will require a recrafting of the relationship the federal government has with Indigenous people to make it work like a respectful partnership.

Laying out his recent move to split Indigenous and Northern Affairs Canada into two separate ministries, Trudeau said he expected Canada's Indigenous people to similarly rethink how they govern themselves.

"For Indigenous peoples, it means taking a hard look at how they define and govern themselves as nations and governments, and how they seek to relate to other orders of government," he said. "Indigenous people will decide how they wish to represent and organize themselves."

Climate change

Linking Indigenous challenges with climate change, Trudeau earned widespread applause from the assembly for saying no country could walk away from the responsibility to address climate change for future generations.

The prime minister said that in communities across the North, Indigenous people were finding sea-ice conditions more dangerous and unpredictable for travelling and hunting in the winter noting that Inuit elders were finding it increasingly difficult to predict the weather.

Describing the country's commitment to climate change internationally as "unwavering," Trudeau said: "Canada will continue to fight for the global plan that has a realistic chance of countering [climate change]"

"We have a chance to build in Canada — and in fact, all around the world — economies that are clean, that are growing, that are forward-looking. We will not let that opportunity pass us by."

Prime Minister Justin Trudeau is shown on big screens inside the UN General Assembly delivering a speech that garnered applause for his pledge to continue to work toward a global climate change deal. (Richard Drew/Associated Press)

It is an unusual move for a head of government to focus their speech to the UN General Assembly on a domestic issue, rather than speaking to a global issue, especially one that highlights a country's own failure to meet the standards it sets for itself.

Trudeau told reporters after the speech that he made the choice because while the venue is normally used by heads of state to talk about what should be done in the world, it is also important to discuss what needs to be done at home.

"A number of times, in conversations over the years, when I have suggested that certain countries need to do better on their own human rights, on their own internal challenges, the response has been; 'tell me about the plight of Indigenous people in Canada.'" Trudeau said.

"I think its actually time we stood up and took responsibility for the terrible mistakes of the past," Trudeau added, saying that the whole purpose of the UN was for countries to "share challenges, perspectives and soloutions."

Fair and progressive trade

Trudeau also used the opportunity to tout his proposed changes to the way small businesses and professionals incorporate and use the tax system to secure advantages.

"Right now, we have a system that encourages wealthy Canadians to use private corporations to pay a lower tax rate than middle class Canadians," Trudeau said. "That's not fair, and we're going to fix it."

Without mentioning the ongoing NAFTA negotiations, Trudeau said his government was working hard to deliver progressive deals such as the Comprehensive Economic and Trade Agreement with the European Union, which came into effect today.

Trudeau said CETA was a deal that could ensure well paying jobs for workers, and economic growth that benefits all Canadians, not just the rich.

"We have the opportunity — and I would argue we have the responsibility — to ensure that trade agreements include strong provisions to safeguard workers' rights, to protect the environment, and to ensure that the benefits of trade are felt more broadly," he said.