Gina Rinehart and her company Hancock Prospecting have threatened to sue the ABC after a filmmaker on television series Race Around the World made a joke about mixing Mrs Rinehart's guts into a sausage roll.
Hancock says it has not received any correspondence from the ABC a week after calling for the broadcaster to remove contestant Kate McGuinness's film.
"The ABC's board and senior management have provided no substantive public response, nor any substantive response to Hancock or Mrs Rinehart," the company said in a statement.
"(The ABC) have taken no steps to remove the material from ABC platforms, despite widespread public condemnation and the serious risks its publication and continued publication pose to Mrs Rinehart."
Hancock says it has sent legal letters to multiple ABC executives, including chair Kim Williams.
The ABC on Friday confirmed it had received the legal letters.
In the film titled A Very Relaxing Video, broadcast on July 12, McGuinness made comments about a possible future revolution in which participants may be "mixing (Mrs Rinehart's) guts up nice and smooth, to make one big sausage roll to make something out of nothing".
In a statement published by the ABC, McGuinness said her comments were not meant to be taken seriously and were not intended to promote violence.
"The sense of humour featured in each of my films on the Race Around The World program is farcical," McGuinness said.
"My writing is cartoonish and always satirical. Unfortunately, jokes do not land with everyone."
Mrs Rinehart's opposition to the comments and her threats of legal action stand in contrast to her previous defence of the right to free speech.
The billionaire has been a longtime supporter and funder of the Institute of Public Affairs, which says "freedom of speech is one of the most important principles of a free society".
In an address on Anzac Day, the 72-year-old said: "If we want to save our country, we need to love it so much that we have the character to stand up and speak truthfully, without hiding in fear of being derided."
The Race Around the World episode was still available to watch on ABC iview on Saturday afternoon.
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