A 19-year-old man has pleaded guilty to the rape and murder of Melbourne comedian Eurydice Dixon whose body was found in a suburban park, sparking a national outcry over women's safety.

Jaymes Todd pleaded guilty to murder, rape, attempted rape and sexual assault in Melbourne Magistrates Court on Thursday.

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Ms Dixon, 22, was found on the Princes Park field at Carlton North by a passer-by about 3am on June 13.

Mr Todd handed himself in to police later the same day.

AAP

In the fallout of her murder, thousands of Australians attended vigils around the country.

Former prime minister Malcolm Turnbull said at a vigil that "this young woman should have been able to walk across the park in her city as safely as she could walk across a room in her home or any public place".

Police warnings at the time resulted in a deluge of criticism and debate about women's safety in public.

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In a statement, Victoria Police's Acting Commander David Clayton said police did not want people to "stop doing their day to day activities".

"However, we do ask all people to consider their personal safety and be aware of their surroundings," he said.

The sentiment has sparked a backlash, with some seeing it as victim blaming.