Opposition Leader Tony Abbott wants tougher legal powers to order "scurrilous" internet bullying attacks to be taken down.
Online bullying is a more disturbing phenomenon than verbal attacks, he said.
"I don't believe in censoring the internet, but we do have to have reasonable protections," Abbott told the Nine Network on Friday.
"What we're looking at is more capacity for take-down orders."
"Every one of these sites is hosted by someone, and if the site is just hosting material that is completely scurrilous ... grotesquely offensive, I think there should be some powers for take-down orders, to ensure people are at least civil to each other."
Early on Thursday morning, TV personality Charlotte Dawson was admitted to hospital after being inundated with abusive tweets telling her to "go hang [herself]" and "put [her] face into a toaster". Shortly before 2am on Thursday, Dawson tweeted that she "hopes this ends the misery" and "you win". Emergency services were called to Dawson's residence in Sydney and she was taken to St Vincent's Hospital, where she is said to be in a stable condition and under observation.
The judge on Australia's Next Top Model came under fire after she had tracked down a Twitter user who had abused a follower and contacted her employer at Monash University in Melbourne to notify the university of the tweets.
Communications Minister Stephen Conroy has called on Twitter to work with Australian authorities to find the "trolls" who attacked Dawson.
"What I would say is that Twitter should cooperate with the police investigation that is now underway to help reveal who these trolls are," Conroy told News Limited.
Social media expert Laurel Papworth said this morning in a blog post that Dawson has a history of "slagging people off" and would be better off blocking abuse on Twitter, rather than "feeding the trolls" by responding to it and retweeting it to her 34,000 followers.
"If you take a bitchy voice, expect a bitchy community; ignore strangers and just block them, surround yourself with people who love you and turn the bloody thing off (Facebook, Twitter) if it disrupts your mood," she said.
In this morning's interview with Abbott, the Twitter abuse was compared to veteran Liberal strategist Grahame Morris' recent attack on ABC presenter Leigh Sales on radio. Morris called Sales a "cow" after she conducted a tough interview with Abbott, during which the opposition leader seemed to say that he'd not read a statement by mining company BHP Billiton.
Abbott said that there was a difference between someone saying "something foolish" and someone posting something nasty online.
"If someone says something foolish, it's out, it's off and it's gone," he said.
"But what happens on social media is, it's there forever, that's the difference — the insult, the offensive words, the incitement and the intimidation is there forever."
Abbott said children who are cyber bullied can't change schools to get away from that culture.
"It follows you on the net," he said. "That's why this is a more disturbing phenomenon."