Senator Jacinta Nampijinpa Price has called for action from the government after the Central Land Council newly appointed chair was revealed to have an extensive criminal history.

During Senate estimates last year, Senator Price, a long-time critic of the CLC, asked about Mr Williams' criminal record, and a month later at a march against domestic violence revealed some of his previous criminal offences, which include domestic violence order breaches, assault, being armed with an offensive weapon.

Some of the offences, which occurred between 2008 and 2015, lead to time in prison.

Senator Price said it was unacceptable Mr Williams - as chair of the CLC plays a role in the closing the gap framework - was "a contributor to the policy process for marginalised Indigenous Australians".

"The government needs to act immediately," she said.

"The Minister [Malarndirri McCarthy] saw fit to intervene in the Anindilyakwa Land Council, when she became aware that there were issues with the board, and she needs to immediately intervene in this case as well.

"How absurd does the situation have to become before we say enough is enough? The Central Land Council is a key organisation in the lives of the most marginalised and vulnerable Australians in the country, and yet it is being run by someone with a serious criminal history."

In a statement on Wednesday morning, Mr Williams said he had made "mistakes" in his life but had "worked hard to turn things around and set things right".

"I regret things I did in the past and have worked hard to make up for them. For the past decade, I've been on a better path, helping others and working to prevent domestic violence in our communities," he said.

Mr Williams, who was elected the chair of the CLC - which represents 24,000 remote Indigenous people across Central Australia - in September, referenced Senator Price's appearance on Australian Story this week, where she outlined her difficulties with drug use after the breakdown of her marriage.

She said, "you can become selfish when you're a drug user", before noting: "I think I could have been a hell of a lot better friend. I treated people badly."

Senator Price managed to get help, which she called "the best thing I could have done for myself because I just needed to pull myself out of that hole".

"I couldn't self-destruct, and I wasn't going to kill myself because of the behaviour and the conduct of somebody else," she said.

Mr Williams said: "As Senator Price has revealed this week, everyone deserves a second chance. I'm using mine to make the world a better place for our families. I would like to be given the same opportunity that Senator Price has sought this week."

"For me, like for Senator Price, giving up alcohol helped make me the person I wanted to be," he said.

Mr Williams argued he was drawing on his life experiences when he talks to men in behavioural workshops.

"The workshops bring together senior community leaders and the police with a range of community support programs," he said.

"Men need to see that change is possible. I teach them that their mistakes don't have to define them. If I can change, they can too. I talk to them about leaving."

Nonetheless, Senator Price was adamant changes needed to be made, reiterating her calls for an audit on all land councils across the country.

"This is yet another example of the racism of low expectations this government applies when it comes to Indigenous organisations and leaders," she said.

"We simply wouldn't stand for this in any other organisation, but for some reason we have a different standard that is applied in cases like these."

The Walpiri/Celtic Senator, who is being sued for defamation by CLC chief executive Les Turner, added: "It's not just the instance of someone with this history having a position of power in a land council, but the circumstances that allow for it to happen."