Social media giant Facebook is refusing a police request to take down hate material posted in response to Jill Meagher's death.
Victoria Police chief commissioner Ken Lay says police asked Facebook to take down a site at the weekend.
"We had cause to speak to Facebook over the weekend and asked them to take a particular site down," Mr Lay told Fairfax Radio this morning.
"Now they have refused to do that so we're just working our way through that about what we can do now."
Mr Lay said that while social media had been very helpful during the investigation, it had also posed difficulties.
"It is disappointing and when you see the hatred that's incited by some of these sites … it is very much the antithesis of what we saw yesterday with 30,000 people taking to the streets saying, 'Let's try and make this a safer and fairer community'.
"We've all got a social responsibility and Facebook is part of our community and I would've thought it would only have been reasonable."
Tens of thousands of Melburnians rallied in Brunswick on Sunday to remember Irish-born Ms Meagher.
A Facebook page was set up to help find the 29-year-old after she disappeared in the early hours of September 22 and several tribute pages were established after her body was found and a suspect charged early Friday morning.
But a number of hate pages directed at the suspect have also been set up, with one attracting 44,000 likes.
Both Ms Meagher's grieving family and Victoria Police have acknowledged the role social media played in the search for the ABC radio employee but police on Friday issued a call for calm, asking people to refrain from posting "inappropriate comments that might jeopardise a successful prosecution".
Ms Meagher's husband Tom also urged people to be cautious in flooding social media sites with negative comments about the accused and the case.
Adrian Ernest Bayley, 41, of Coburg has been charged with Ms Meagher's rape and murder. He is in custody awaiting a committal mention hearing on January 18.
Comment is being sought from Corrections Victoria regarding a newspaper report Bayley is being moved to higher security in jail amid fears he will be attacked by other inmates.