In an editorial, The Australian newspaper defended the illustration and pointed to the substantial resources it dedicates to covering Indigenous affairs.
"The cartoon points to broken families, the self-perpetuating cause of so much Indigenous misery," it said.
"One great obstacle to improvement is the progressive tendency to look away from awkward truths: to prefer their moral vanity over better outcomes for others; and to expend energy on policing 'incorrect' commentary rather than championing needed reforms."
A recent news report showed juvenile detainees in Australia's far north being stripped, sprayed with tear gas and, in one case, cuffed to a chair while forced to wear a hood.
Prime Minister Malcolm Turnbull promised an investigation, saying he was "shocked and appalled" by the footage.
The original illustration was criticised by Indigenous groups, politicians and on social media.
Indigenous Affairs Minister Nigel Scullion said he was appalled by the publication of the "racist" cartoon in The Australian.
"Although Australian cartoonists have a rich tradition of irreverent satire, there is absolutely no place for depicting racist stereotypes," he said.
"I would urge The Australian to be more aware of the impact cartoons like the one published today can have on Indigenous communities."
Greens leader Richard di Natale called the cartoon "disgraceful" and reminiscent of attitudes from a bygone era.
"I've written to the editors of The Australian newspaper asking them to apologise for those awful stereotypes," he said.
"Fancy a cartoon implying that Aboriginal parents don't love their children."
'Howls of outrage'
After widespread condemnation on social media, cartoonist Leak adapted his original cartoon to show himself being handed over to a man wearing a Twitter T-shirt and carrying a baseball bat and a noose.
He also defended his work in a column, claiming to speak the truth about violence and abuse in Indigenous communities.
"I was trying to say that if you think things are pretty crook for the children locked up in the Northern Territory's Don Dale Youth Detention Centre, you should have a look at the homes they came from," Mr Leak wrote.
"Then you might understand why so many of them finished up there."
The Australian also ran a column from Marcia Langton, the chair of Australian indigenous studies at the University of Melbourne in which she faulted indigenous leaders for their silence on personal responsibility.
"This is not a race issue but one that requires an understanding of how difficult it is to deal with children who have been failed by their families to such an extent that they become child criminals," she said.
However, she told The Guardian that she did not intend for her opinions to be used in the defence of the cartoon.
"I am not 'comfortable' with my words being used to justify Leak's cartoon," she said.