Communications Minister Stephen Conroy says Twitter is acting as though it is above the law.

He made the comments as concern increases about the online bullying, abuse and harassment known as trolling.

One communications law expert has also called on Twitter to open an Australian office and become more accountable.

It is a criminal offence to make a death threat using the internet or a carriage service and it has imprisonment of up to 10 years.

Making someone apprehensive is also a criminal offence, with possible jail terms of up to three years for menacing, harassing or offending somebody.

Professor Michael Fraser, director of the Communications Law Centre at the University of Technology Sydney, says attacking somebody is not freedom of speech.

"It is the opposite of freedom of speech," he told The World Today.

In the wake of high-profile cyber bullying cases, Senator Conroy has been trying to contact Twitter - with no luck.

"We've all been trying to raise these points but they are so arrogant they consider that they don't have to take any notice," he told Channel Nine.

"Twitter, an American company, they think they are above our laws, they think they are above laws in America.

"They just believe they don't have to take any notice of the Australian public, any notice of the Australian laws and they think they can behave this arrogantly."

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Twitter does not have a phone number and no-one from Twitter responded to The World Today's email this morning.

Professor Fraser says Twitter needs to step up to the mark.

"They are operating in jurisdictions all around the world and they need to be accountable for making their social media network a safe place for their clients," he said.

"I think the first thing they should do is to open an office in our jurisdiction and respond to requests from government and law enforcement agencies... so criminals can't hide behind anonymity.

"We don't want companies giving away people's private information unless there is a due process involved," he said.

"But I don't think they are being very cooperative in working out a reasonable process so that when law enforcement has a reasonable suspicion and gets a warrant or a subpoena, they can rapidly address these problems.

"After all, all criminals want to hide behind the mask of anonymity and we shouldn't make it easy for them to do that."