"What is it in our community that allows some men to think that it's still OK to attack women or take from women what they want?" Mr Cornelius said. "Violence against women is absolutely about men's behaviour."
Mr Cornelius said he often reflects, in these situations "on what advice I may give my wife or my daughter".
"The advice that I give them is that we're in a very safe city," he said.
"There have been instances in our recent past where women have been attacked and they have been attacked by men.
"And the key point I'd make about that is that this is about men's behaviour, it isn't about women's behaviour.
"Violence against women is absolutely about men's behaviour."
He said it was up to society to change the attitudes of some men.
Victorian Premier Daniel Andrews agreed that men's attitudes to women need to change.
"This is a terrible tragedy," Mr Andrews told reporters on Sunday.
The Premier, who delivered Australia's first royal commission into family violence the last term, said while the state had made significant progress on violence against women, there was more to be done.
"This is not about the way women behave. This is not about where women are at what hour," he said."This is most likely about the behaviour of men."
On Monday, the new Minister for Women Marise Payne - who is also Minister for Foreign Affairs - following her appointment on Sunday by Prime Minister Scott Morrison - said that the safety of women will be a top priority for the federal government.
"We have been only too tragically reminded in the last couple of days, again in Melbourne with the appalling murder of Courtney Herron, that the safety of women is something that must concern us all," she told ABC radio on Monday.
Anyone with any information should contact Crime Stoppers on 1800 333 000.