A United Nations investigator probing discrimination against Native Americans has called on the US government to return some of the land stolen from Indian tribes as a step toward combatting continuing and systemic racial discrimination.

Close to a million people live on the US's 310 Native American reservations. Some tribes have done well from a boom in casinos on reservations but most have not.

Anaya visited an Oglala Sioux reservation where the per capita income is around $7,000 a year, less than one-sixth of the national average, and life expectancy is about 50 years.

The two Sioux reservations in South Dakota – Rosebud and Pine Ridge – have some of the country's poorest living conditions, including mass unemployment and the highest suicide rate in the western hemisphere with an epidemic of teenagers killing themselves.

"You can see they're in a somewhat precarious situation in terms of their basic existence and the stability of their communities given that precarious land tenure situation. It's not like they have large fisheries as a resource base to sustain them. In basic economic terms it's a very difficult situation. You have upwards of 70% unemployment on the reservation and all kinds of social ills accompanying that. Very tough condition."

Anaya said Rosebud is an example where returning land taken by the US government could improve a tribe's fortunes as well as contribute to a "process of reconciliation".

"At Rosebud, that's a situation where indigenous people have seen over time encroachment on to their land and they've lost vast territories and there have been clear instances of broken treaty promises. It's undisputed that the Black Hills was guaranteed them by treaty and that treaty was just outright violated by the United States in the 1900s. That has been recognised by the United States supreme court," he said.