The scheme is the centrepiece reform in an exposure draft of the Online Safety Bill,which Communications Minister Paul Fletcher will release for consultation on Wednesday.
Mr Fletcher said the scheme would address a gap in the law,as the eSafety Commissioner can issue take-down notices only for abusive material targeting children.
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"We do not have,at the moment,legal powers when a complaint is made to the e-Safety Commissioner by an adult who has been the subject of vicious online abuse,"Mr Fletcher said.
He said the proposed legislation would capture abuse constituting"serious harm",such as threats to rape and kill and racist attacks,providing the abuse was targeted towards particular adults rather than generalised abuse.
The bill will set a higher legal test for what constitutes abuse directed at adults compared with children.
"That's because first of all adults are more resilient than children,but secondly we need to strike the right balance with freedom of speech,"Mr Fletcher said.