"I had an email from her this morning. Above all what she wants is that it does not become a row about xenophobia because it isn't one," Annie Desaintjores, an aunt of Fanny Desaintjores, told AFP.
"The scene was filmed by an amateur who made a big deal of it," she added.
"It has been depicted as an example of xenophobia but, as she said in her email, worse things happen in France and it doesn't become a diplomatic incident. It has also been blown out of all proportion by the media and that's a shame."
The aunt added that her 22-year-old niece had no intention of cutting short her stay of up to nine months in Australia.
Melbourne police are investigating the incident in which Fanny Desaintjores was on the end of a torrent of threatening abuse from other passengers on the bus, who were apparently provoked by her singing in French.
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One demanded she "speak English or die" and threatened to cut her breasts off while another man shouted: "I'll fucking boxcutter (knife) you right now, dog."
Ted Baillieu, the premier of the Australian state of Victoria, has condemned the incident as "absolutely disgraceful" and urged the public to help identify those responsible.