Both sides of parliament admit successive governments have failed Indigenous people as new data shows the disadvantage gap continues to widen.

The admissions from the major political parties came as Productivity Commission figures show a number of key Closing the Gap targets are not on track, with the majority going backwards.

Closing the Gap is a strategy that aims to achieve equality for Indigenous people by improving health, social, education and economic outcomes.

Indigenous senator Lidia Thorpe told parliament the same pressures her great grandmother faced to reject her Aboriginal heritage persisted.

"The government's policy of the day was to assimilate our people who had mixed heritage," the independent senator said.

"My great grandmother was subjected to that. We still see that happening in this country today."

Minister for Indigenous Australians Linda Burney admitted the gap between Aboriginal and Torres Strait Islander people and other Australians is not closing fast enough.

"I know many people are frustrated by the lack of progress," Ms Burney said.

Foreign Minister Penny Wong said bureaucrats had made policies without consulting Indigenous communities for too long and senior Liberal frontbencher Simon Birmingham said it was a "stain on Australia" that the gap existed.

The federal government has put more than $400 million in extra funding towards its implementation plan to close the gap.

There are 19 socio-economic targets in the National Agreement on Closing the Gap.

The Productivity Commission has released data on nine of those targets, which shows only two are on track to meet their goals: employment of Indigenous adults and land rights.

Seven are not on target, including babies with a healthy birth weight, finishing Year 12, appropriate housing and reducing suicide rates.

Ms Burney said while there were "encouraging" increases in employment and land rights, more of the same wasn't good enough with figures going backwards in other areas.

Indigenous Labor senator Pat Dodson said Australia should never forget its history, "the good, the bad and the ugly".

"We also need tangible action to address the poor outcomes for Aboriginal and Torres Strait Islander people," Senator Dodson said.

First Nations Greens senator Dorinda Cox said colonisation had changed how Indigenous people connected with their land, their culture and their community, with racist policies resulting in catastrophic outcomes.

"We get sicker, we die earlier. We are poorer. We are arrested and locked up more and we have our children taken away from us," she said.

Senator Thorpe said the gap couldn't be closed by the same institutions that uphold disadvantage.

"Real support cannot be provided by just another one of your colonial institutions where black fellas don't feel safe," she said.

Country Liberal Party senator and Indigenous woman Jacinta Price said the lives of Indigenous children in rural Australia "are being left in dysfunctional circumstances because of their race".

The inaugural ambassador for First Nations people Justin Mohamed has also been announced as the government seeks to increase its engagement on issues facing Indigenous people in the Pacific.