Barker gained notoriety early last year after trolling the Facebook page of pop star Nicki Minaj with an abusive rant that attracted more than 100,000 "likes".
In another rant, Barker called on his followers to harass Muslim families by making prank telephone calls.
He said he used White Pages to search for a family with the Ibrahim surname and phoned to joke a packet of bacon had been placed on the family's doorstep.
"I picked one at random," he said. "It was hilarious." Followers of Barker made similar calls at his request.
Detective Senior Constable Rodney Andrew, from Melbourne police, said their inquiry had stalled as Barker was out of the country.
Netsafe executive director Martin Cocker said it was his opinion that Barker's actions were "inciting acts of hatred".
"The internet is empowering everybody, including those who have a message we'd rather not hear," he said.
Internet trolls tried to get attention and a response from people by being as offensive and outrageous as possible, he said.
"There's always a group of people in society who want to do that, who don't have a way of achieving recognition in a positive way."
Cocker advised people to not engage with trolls.
Justice Minister Judith Collins is expected to outline new measures to curb cyber-bullying within the next few weeks.
The minister had earlier asked the Law Commission to fast-track a review of the laws around telecommunications and the internet.
In Australia, ex-police officer and internet commentator Susan McLean said she believed Barker was "Australia's most prolific troll".
"He has no concept of common decency and is a blight on society."
