An exchange student killed after alighting a Melbourne tram was ambushed as she chatted with her sister by phone, police have revealed, with known sex offenders under suspicion over the "horrific attack".
It was just after midnight on Wednesday morning when the call dropped out, prompting 21-year-old Aiia Maasarwe's sibling to raise the alarm from overseas after a desperate attempt to ring her back failed.
Detectives are meanwhile scouring records of known sex offenders as they hunt the person responsible for the fatal assault of the young Israeli woman, in north suburban Bundoora.
"This was an horrendous, horrific attack inflicted on a completely innocent young woman who was a visitor to our city," Detective Inspector Andrew Stamper told reporters as he pleaded for public help to solve the crime.
Ms Maasarwe had spent the evening at The Comic's Lounge before being dropped to the tram by friends.
Her body was found in scrub near a shopping centre by passers by about 7am.
"We're looking at everyone at the moment. Known sex offenders are an active line of inquiry as well," Insp Stamper said, adding that the case is being treated as a random attack.
A black baseball cap emblazoned with '1986' and a Cotton On brand light grey t-shirt with dark colours on the shoulders and sleeves, were found at the scene and are believed to belong to the killer.
"Out of respect of the family, we're not going into details of the injuries and the nature of the assault," the detective said, as he awaits the results of a post-mortem examination to determine the cause of death.
Ms Maasarwe was carrying a bag when assaulted and some items had been removed and were found nearby, police said.
Images of the victim showing her appearance on the evening and of the cap and t-shirt have been made public.
"The answers are in the community," Insp Stamper said.
"We need someone in the community to know something about this and we need them to be accountable for this ... for actually delivering this person to us or information about them, so we can get this person off the streets."
Members of Ms Maasarwe's family have arrived in Melbourne and it's believed her body will be repatriated.
A relative told ABC TV the family had considered Australia a safe place.
Police continued to search the area on Thursday and still want to speak to anyone who travelled on a route 86 tram from the city to Bundoora late on Tuesday.
La Trobe University, where Ms Maasarwe studied at an on-campus college, is offering staff and students after-dark security escorts and has boosted patrols at the campus, where everyone is "shocked and saddened by this appalling crime".
Health Minister Jenny Mikakos said the Victorian government would do whatever was required to support Ms Maasarwe's woman's family and friends.
Members of the public are leaving flowers and cards nearby where she was found.
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