Trudeau told the UN General Assembly that Canada's 1.2 million Indigenous people had mostly known "humiliation, neglect and abuse" in a country often held up as shining example of diversity.
"We know that the world expects Canada to strictly adhere to international human rights standards," said Trudeau, who has put reconciliation with First Nations at the top of his reform agenda.
"That is what we expect of ourselves, too."
Trudeau drew applause when he pledged Canada's "unwavering" support to global efforts to combat global warming which he said was affecting the lifestyles of Inuit communities in the north.
Canada's permafrost is melting in the Arctic and "huge pieces of tundra" are eroding into the ocean, he said.
Trudeau also took an implicit swipe at the United States over its withdrawal from the Paris agreement on climate change.
"There is no country on this planet that can walk away from the reality of climate change," said Trudeau, alternating between French and English in his remarks.
It was Trudeau's second address to the world body following his 2015 election.
"Canada is no land of wonders where hardships that you know do not exist," said the prime minister, whose country consistently ranks among the world's highest in living standards.
"Canada remains a work in progress," he declared.