Just 11.7 per cent of Aboriginal and Torres Strait Islander people have been fully vaccinated, while one in five of Australia's entire population have received two doses.

A quarter of the Indigenous population has received a first shot, compared with 41.4 per cent of all Australians.

The prime minister noted no Indigenous person had died from coronavirus during the pandemic, after being quizzed about the lower rates.

"There are remaining vulnerable communities within the country that we will continue to have to take a very bespoke approach, a very customised approach," Mr Morrison told reporters in Canberra on Thursday.

"That is certainly true for Indigenous communities.

"We will work with the Indigenous health sector to ensure that we can deliver on that very customised approach."

Indigenous people were identified as a high priority because of higher rates of chronic health conditions.

All Aboriginal and Torres Strait Islander people are eligible for coronavirus jabs.

Senior Aboriginal leader Pat Turner said remote communities with highly concentrated and impoverished Indigenous populations living in overcrowded housing were particularly important.

"We need 100 per cent vaccination of all Aboriginal and Torres Strait Islander people, no matter where they live," she said.

"We just can't afford for any strain of COVID getting in."

The federal government has also blamed misinformation spread by anti-vaxxers on social media for low immunisation rates of Indigenous people.

Vaccine rollout commander John Frewen said ensuring Indigenous people were protected was a priority.

"I'd always like more to be done and I'd like it to be done faster but we're working with the appropriate authorities," he said.

Lieutenant General Frewen said some communities had progressed quickly but others would need more work.

Australian Associated Press