Labor and the Greens are at odds over whether action needs to be taken against Twitter trolls.
While both parties agree there is no place for cyberbullying, the Greens say additional government intervention is not needed.
But the federal government has congratulated The Daily Telegraph for launching a campaign to catch trolls who post abusive messages.
Communications Minister Stephen Conroy says abusive and harassing behaviour on social networking sites, such as Twitter, could have devastating consequences.
Attorney-General Nicola Roxon said cyberbullying had no place in society.
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"It is against the law to use social media in a harassing way," she said.
What was needed was strong co-operation from governments, law enforcement and the community, Ms Roxon said.
"But we also need the assistance of US-based social networks like Twitter."
Australian Greens senator Scott Ludlam said it was good to shine a spotlight on some of the cowardly behaviour that's become normalised online.
"This is hardly a place for additional government intervention though," he said.
In a dig at The Telegraph, he said it was ironic the same media platforms that ran a freedom-of-speech campaign against media reforms were now demanding a legislated crackdown on individuals' behaviour online.
"They are the same platforms that have stayed silent about proposals to spy on the communications of every Australian, and are the same ones that publish some of the most vitriolic and abusive comments," he said.
