A public memorial for comedian Eurydice Dixon, who was killed in inner-city Melbourne last week, has been vandalised with offensive paint markings.

Police said the paint markings were found at the site in Princes Park during routine patrols just before 4:00am.

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Floral tributes were not disturbed, but police said a number of items were seized from the scene and the dog squad had been through the area.

Firefighters were called in and removed the paint with a high pressure hose.

"It's lower than low, it's the absolute pits," said Sue Murray, who was walking her dog in the area.

Victoria Police Chief Commissioner Graham Ashton said there was a lot of CCTV in the area which he hoped would help police find the culprit, or culprits.

"[It's] terrible really, shocking," he told ABC News Breakfast.

Megan Bridger-Darling, one of the vigil organisers, said she was "mortified" by the vandalism.

"I would never have expected something so vile to happen in such a sacred place, at such an important time," she said.

"I'm genuinely disgusted that this happens in our society and that we have created a culture where this is funny. It is absolutely galling."

Eurydice Dixon has been remembered by friends as a kind and talented comedian. ( Supplied: Facebook )

Mr Ashton also conceded officers should have been more careful with their language when warning people to take responsibility for their safety after the killing last week, which sparked a public backlash.

"Certainly for police when we're giving out public safety messages we need to be really careful about how we do that," he said.

"If our language is not right, or isn't precise, we understand that that can lead to a lot of anger.

"We weren't about victim blaming and we certainly agree absolutely that women, and men for that matter, should have the right to walk around these public spaces when they want to walk around them, and do so safely."

Firefighters were called removed the offensive vandalism from the memorial site. ( ABC News: Scott Jewell )

Police to review safety in park

Debate about gendered violence and security in Melbourne has been front and centre in the days since Ms Dixon's death.

Police today briefed Melbourne Lord Mayor Sally Capp on measures to improve safety and security in the city.

Assistant Commissioner Stephen Leane said police would conduct a safety assessment of Princes Park over the next month in response to Ms Dixon's death.

"We have conducted many of these [assessments] across Melbourne over the last decade or so," he said.

"They've led to changes across places like Birrarung Marr and the Yarra River precincts … we'll use that knowledge that we've learnt across public space to put that in place."

Ms Capp said the meeting also discussed the planned expansion of security cameras in the CBD, a measure already underway in the wake of the Bourke St incident.

"We know that random acts of violence are difficult to predict, but one of the aspects from this morning that I'm very pleased about is the existing investment in CCTV and what is going to be increased investment … both in terms of number of cameras and the capability of those cameras," she said.

"That will be instrument both in terms of predictive elements of crime but also in deterrent of crime."

Police Minister Lisa Neville, who also attended the meeting, said Melbourne was a "very safe" city, which is why the community had been left "shocked" by the violent crime.

"That sort of stranger violence against women happens at low levels but this sort of serious, significant event that we saw last week is rare," Ms Neville said.

"That's why we are so rightly shocked and left grieving.

"We all have a role as a community to start to tackle those underlying attitudes that some men have to women in our community."

Eurydice Dixon was described as having a promising career in stand-up comedy ahead of her. ( Facebook: Paula Ferrari )

Vigils across Australia set to draw thousands

Thousands of people are expected to attend vigils in parks across Australia this evening after Ms Dixon's body was found last Wednesday.

Broadmeadows man Jaymes Todd, 19, has been charged with the rape and murder of Ms Dixon,

More than 10,000 people have indicated they will attend a vigil planned at Princes Park on Monday night.

Ms Bridger-Darling, said the event was about providing a place for the community to come together to show respect, love and solidarity.

"It's a way of saying this is our park, and we feel safe here, this is our soccer pitch … this is our area," she said.

"And you can't take that away through fear."

Park vigils have also been organised in other capital cities, including Sydney, Adelaide, Perth and Hobart.

Vigils will also be held in the regional Victorian cities of Geelong, Ballarat, Bendigo, Albury-Wodonga and Castlemaine, as well as Devonport and Launceston in Tasmania.

Ms Bridger-Darling said she was moved by people in cities around the country creating their own park vigils.

10,000 people say they will join the vigil at the park where Ms Dixon's body was found. ( ABC News: Zalika Rizmal )

"That is a beautiful way of showing just how much one person's life can ripple out and echo around the country," she said.

"They're parents worried about their children, they're brothers and sisters worried about their families.

"What has happened has resonated with a lot of people."

Ms Bridger-Darling said the response also reflects wider concerns about violence against women, victim blaming and public safety.

"I think in the last 12 months, with the #MeToo movement and women standing up and saying — OK enough no more — the line has been drawn," she said.

"Unfortunately it's taken this tragedy to have this conversation."