Colin Barnett said yesterday that laws against online harassment were "almost impossible" to enforce.
The Premier's comment came after the admission to hospital of television host Charlotte Dawson after a Twitter attack exposed conflict between State and Federal authorities over who was responsible for punishing online harassers.
Under Commonwealth law, using a telecommunications service to "menace, harass or cause offence" is punishable by three years jail, but Australian Federal Police said yesterday it was up to State authorities to pursue complaints.
A WA Police spokeswoman said she was unaware of the agency ever charging anyone.
Dawson, a judge on a TV modelling competition who has battled depression and attracted past criticism on Twitter, faced an escalation of the abuse this week, including multiple calls for her to kill herself.
Early on Thursday, Dawson, who campaigns against cyber bullying by retweeting abusive posts, posted "Hope this ends the misery" and "You win x".
An ambulance arrived an hour later and she was taken to the emergency psychiatric care unit at St Vincent's Hospital in Sydney.
Dawson briefly left the hospital on Thursday to conduct an interview with a 60 Minutes reporter for a story on online bullying.
Communications Minister Stephen Conroy blamed Twitter for failing to help track down abusive internet "trolls".
Opposition Leader Tony Abbott called for greater powers to close sites that hosted "grotesquely offensive material".
Mr Barnett said: "I think enforcement is almost impossible. It's rather about encouraging proper, sensible, considerate use of online methods. You can't stop people and kids doing the wrong thing but you can help educate the majority."
University of WA social media expert David Glance said rather than responding to or re-tweeting the abuse, Dawson should have blocked the offenders."There's a saying, 'Don't feed the trolls'," he said.
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