The family of a West Australian woman who died while in police custody in the Pilbara have been granted a $1.1 million ex-gratia payment and given an apology by the State Government.

Attorney-General John Quigley confirmed the payment to the family of Ms Dhu, a 22-year-old who died while being held in custody in South Hedland over unpaid fines in 2014.

The payment — which will be split between five relatives of Ms Dhu — will not stop the family from seeking further damages through legal action.

Ms Dhu's death sparked widespread outrage and was the subject of a coronial investigation which labelled the police treatment of her "inhumane".

She died on her third visit within 48 hours to Headland Health Campus after complaining of feeling unwell while in custody. She was found to have died of septicaemia and pneumonia.

The coroner said Ms Dhu's life could have been saved had doctors properly diagnosed her.

Space to play or pause, M to mute, left and right arrows to seek, up and down arrows for volume. Watch Duration: 1 minute 10 seconds 1 m 10 s Ms Dhu died in police custody

Mr Quigley said Ms Dhu's family had "suffered considerable trauma".

"I have met with three of Ms Dhu's very close family and have personally offered the state's sincerest apologies for the circumstances leading to the death," he said.

Dhu family 'pleased': Attorney-General

Ms Dhu's family have flagged civil legal action against the state — with her mother saying no-one had been held accountable for what happened — and Mr Quigley said the ex-gratia payment would not restrict that.

Sorry, this video has expired Ms Dhu's mother Della Roe says she wants "someone [to] pay for what they did to my baby".

But he said the $1.1 million payment would be deducted from any future damages awarded.

"Whether they take other action, who knows, but they were pleased with the Government's response," Mr Quigley said.

The Attorney-General pointed to moves to introduce a custody notification service, which would require police to call a hotline whenever an Indigenous person was arrested.

"Had such a service been in operation at the time, the tragedy may well have been avoided and Ms Dhu part of our world today," Mr Quigley said.

Mr Quigley also confirmed an ex-gratia payment request had been lodged by Gene Gibson, who was wrongfully convicted of the manslaughter of a man in Broome.

Lawyers for Mr Gibson, who spent more than five years in jail, have previously said they were seeking a $2.5 million payment.

The application is still being considered by the State Solicitor's Office.