The senior Aboriginal women of Coober Pedy, in outback South Australia, have condemned the Federal Government for choosing to set up a low-level nuclear waste dump in the state.

A sheep station near Woomera has been picked to host the national low-grade repository.

However, the Federal Government has ruled out setting up a medium-level dump in South Australia.

The Kupa Piti Kungka Tjuta Council says it has no comfort from the decision to set up a higher level dump in another state, because "poison will still being going underground" in their area via the low-level dump.

Spokeswoman Nina Brown says the women recently won the international Goldman Prize for all the work they have done to try to stop the dump and it has been in vain as far as the Federal Government is concerned.

"They finally get this international acclaim and the Government disrespects their rights as Aboriginal elders in the community and just overrides their concern for country and their communities," she said.

The women have pledged to keep working to stop the low-level dump from being established in South Australia.