A US federal judge has approved a $3.4bn settlement over "mismanaged" Native American royalties, in a case that represents the largest settlement ever approved against the US government.

Elouise Cobell of Browning, Montana, claimed in the 15-year-old suit that for more than a century, US officials systematically stole or squandered billions in royalties intended for Native Americans in exchange for oil, gas, grazing and other leases.

Thomas Hogan, the US district judge, approved the settlement on Monday after a daylong hearing, saying the legitimacy of Cobell's claims could not be questioned.

"The government mismanaged these resources on a staggering scale," Hogan said.

The settlement does not make up for the losses native American tribes suffered for more than a century, Hogan added, but "at least it provides some certainty" to hundreds of thousands of individuals who will now receive payments of least $1,000 each from the government. Many will receive substantially more money.

Cobell, a member of the Blackfoot Tribe, will receive $2 million, and three other named plaintiffs will receive payments ranging from $150,000 to $200,000 each.