A Bill Leak cartoon published in The Australian newspaper on Thursday depicts an Aboriginal man who has forgotten his son's name.
Indigenous groups said the cartoon was "ugly, insulting and embarrassing".
But the paper's editor said the cartoon brought a "crucial issue" into the public domain.
In the cartoon, a police officer is shown bringing an Indigenous child to his father, saying: "You'll have to sit down and talk to your son about personal responsibility."
The father, who is barefoot and holding a beer can, asks: "What's his name then?"