The state government will establish a Custody Notification Service which will ensure a representative from the Aboriginal Legal Rights Movement is contacted in relation to all custody cases.

Attorney-General Vickie Chapman says the service will help ensure Aboriginal people receive culturally appropriate wellbeing support and basic legal advice as soon as possible.

"While we have had similar arrangements in place for quite some time, there have never been any formalised legislative measures," Ms Chapman said.

"This will also bring us in line with other jurisdictions around the country who have legislated for these measures."

Ms Chapman said harsher penalties for officers who failed to comply were also proposed under the service.

"A representative from the Aboriginal Legal Rights Movement must be allowed to speak to or visit the Aboriginal person, and discuss any concerns regarding their welfare, including whether they need an interpreter or support person," she said.

"One of the most significant measures we're also proposing is if a responsible officer refuses or fails to comply with these requirements, they may be subject to disciplinary proceedings."

Ms Chapman said the government would continue to work closely with the Aboriginal Legal Rights Movement to determine the proposed scope and model of the service.

"Eliminating Aboriginal deaths in custody is paramount, and these measures are a further step towards that," she said.

More than 5000 people attended the Black Lives Matter Rally in Adelaide's CBD last month, held in part to raise awareness of the continued death of Aboriginal people in custody.

Another rally is scheduled in Adelaide on Saturday.

Australian Associated Press