Pope Francis has made a long-awaited and historic apology to Indigenous people for the Catholic church's role in abuse and "cultural genocide" at Canada's residential schools.

In an address to Indigenous leaders after meetings with Métis, Inuit and First Nations delegates, Francis said the behaviour of church members at residential schools run for more than 150 years was deplorable.

Speaking in Italian, Francis said he hoped to visit Canada in July following his apology.

"For the deplorable behaviour of those members of the Catholic Church, I ask forgiveness from God and I would like to tell you from the bottom of my heart that I am very pained," he said.

"I join my brother Canadian bishops in apologising."

One of the Indigenous leaders said he wanted the Pope to make the apology on Canadian soil.

Canadian Prime Minister Justin Trudeau welcomed the apology, calling it a "step forward" in acknowledging the truth of Canada's past, but said there was still work to be done.

"We look forward to him coming to Canada to deliver that apology in person," he said.

"Canada's history will forever be stained by the tragic reality of the residential school system.

"As a country, we must never forget the unthinkable tragedies that took place and we must honour the children who went missing and never came home."

About 150,000 Indigenous, Metis and Inuit children were forcibly enrolled from the late 1800s to the 1990s in 139 residential schools across Canada.

They spent months or years isolated from their families, language and culture, and suffered from horrific abuse, which was labelled cultural genocide in 2015 by the Truth and Reconciliation Commission.

Since last May there have been about 1,300 discoveries of unmarked student graves at several of the former schools.

There are ongoing searches expected to uncover many more.