Shine Lawyers on Wednesday said in a statement it would take on the case, with up to 6000 Indigenous Australians eligible to join the class action filed in the NSW Supreme Court.

Special counsel Tristan Gaven, who will legally represent the group, said most states had taken steps to compensate stolen generation survivors but no such action had occurred in NT.

Compensation will be sought for the forced removal of Indigenous Australians from their families between 1910 and the 1970s.

"It's impossible to improve the future without acknowledging the past," Mr Gaven said.

"The Commonwealth was responsible for tearing apart Indigenous families in the Territory and it's up to the Commonwealth to make amends."

Litigation Lending Services, which is financing the class action, said the injustice of the NT stolen generations is yet to be resolved.

LLS director Warren Mundine said in a statement: "If this was to happen today, there would be serious public global outrage and criminal charges laid on all involved for these barbaric acts."

The matter is listed for first directions on June 17.

One member of the class action, 84-year-old Heather Alley, was nine years old when forcibly removed from her mother and transported from Mataranka to western Sydney.

She later lived in an Alice Springs hostel, where she was flogged.

"I couldn't understand why this was allowed to happen and I was very broken for many years," Ms Alley said in a statement.

Federal Indigenous Australians Minister Ken Wyatt has been approached for comment.

Labor Indigenous Australian spokeswoman Linda Burney told reporters on Wednesday her party supported compensation for members of the stolen generation living in the capital territories.

"The commitment of our party is to compensate those where there has been no compensation scheme in place," Ms Burney said.

Australian Associated Press