If the Harmful Digital Communications Bill is passed an agency will be set up to deal with complaints about online behaviour.
The issue of online abusive erupted last week with the Roast Busters scandal in Auckland.
But Mr Keown, who lost his seat on the city council at last month's local body elections, but still remains a member of the Shirley-Papanui Community Board and Canterbury District Health Board, was unrepentant.
He told The Star that the woman who allegedly left an abusive message for him should be prepared to take it as well.
The message left on his phone related to him losing his city council seat.
The Star tried to ring the woman yesterday but her mail box was full.
On his Facebook page, Mr Keown told people: "... if you are bored feel free to send her abusive messages or do a crank call, its obviously what she's into."
It is the second time in recent months Mr Keown has drawn criticism over his Facebook posts.
Mr Keown was investigated by Solicitor-General Michael Heron QC in July after posting a link on his Facebook page which revealed the identity of the men who attacked cricketer Jesse Ryder outside a Merivale bar. They had name suppression at the time.
Mr Keown told The Star public figures often received abuse and identifying abusers was the best way to stop what he saw as a growing problem.
Deputy Mayor Vicki Buck said the post was "not okay for anyone".
"It's not in the slightest bit helpful, especially for an elected member," she said.
Mr Keown said he had "mulled over" what to do with the number, but decided to give abusers a "taste of their own medicine."
"I'm going to start posting some of them, so that other people can see who they are."
Canterbury University Law Professor Ursula Cheer said a gap in the law meant Mr Keown's behaviour may not be illegal but could be under new legislation.
The Harmful Digital Communications Bill, introduced to Parliament last week, would make sending messages or posting material online with intent to cause harm an offence.
"It's unacceptable behaviour professionally. For someone who holds a community position, it shows a lot about their character and lack of judgement," Professor Cheer said.
Shirley-Papanui Community Board chairman Mike Davidson said he disagreed with the choice to publish details of abusers and would be raising the incident with Mr Keown.
"I think it's best to go through the right channels and not just retaliate to that type of abuse, it doesn't achieve anything," he said.
