The measures are the linchpin of aproposed new adult cyber abuse scheme,announced by Communications Minister Paul Fletcher as a"world first"on Wednesday.
Ms Inman Grant said the scheme,which the government hopes to legislate next year,would give her a range of enforcement powers from formal warnings to fines,adding that perpetual abusers were now on notice.
"Those are the types of people that we would likely target with these harsher penalties,"Ms Inman Grant said.
"We will be given new powers to be able to compel the platforms to provide us with more account information,so that we can at least service notices or try to establish identities in a much more better fashion than we can today."
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The Office of the e-safety Commissioner was established in 2015 as a world-first government agency dedicated to regulating online safety. Ms Inman Grant was appointed as the inaugural commissioner in 2017.
The agency's data shows that from March to September this year,there was a 49 per cent increase in adult cyber abuse and a 32 per cent increase in youth-based cyber bullying compared to the monthly average for 2019.