The body was identified as Aya Masarwe by an Israeli newspaper this morning (Masarwe was a university student on exchange in Australia).
Police would not confirm reports they were investigating a sexual assault but said known sex offenders are an "active line of enquiry".
Authorities have increased patrols and police escorts around Bundoora since Maasarwe's body was found.
A distinctive black cap with the number "1986" and a two-tone grey Cotton On T-shirt dumped after the attack and found by police less than 100 metres from Maasarwe's body now hold the key to catching the killer.
Investigators say Miss Maasarwe was at the Comic's Lounge club in North Melbourne earlier that night, and was driven by friends into Bourke Street, where she boarded the 86 tram about 10.50pm.
Her uncle, Rame Maasarwe, told the Guardian she was on a video call with her sister at the time of the attack. She was on an exchange programme at LaTrobe, he said.
Detective Inspector Andrew Stamper said Thursday that further details about her injuries would not be revealed out of respect for her family.
"This was an absolutely horrendous, horrific attack inflicted on a completely innocent young woman who was a visitor to our city", he added.
"She was actually involved in a conversation with her sister overseas at the time the attack took place".
Her death provoked an outpouring of grief, with more than 5,000 people attending a vigil at the park, and a wider push by police to acknowledge that women should be free to come home alone late at night and be safe.
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"I was in shock, I couldn't believe it... the day before my wife had said to me, 'We'll have to go to Australia, Australia's very safe, very nice, '" the victim's uncle Rame Maasarwe told national broadcaster ABC from the United States.
Dozens of locals visited the crime scene on Thursday to lay flowers and remember the young student who in recent weeks had posted shots of her first sunrise of 2019, as well as Australian waterfalls and bushland.
"We have complete faith in the Victorian Police and have no doubt that they will leave no stone unturned in the search to bring the perpetrator to justice", it said in a statement.
Maasarwe's body was found on Wednesday morning by passers-by at 7am about 50m from the stop where she exited the tram.
Stamper said detectives were desperate for members of the public to provide information about the shocking crime, which sent shockwaves across the city and Israel.
"We have a grieving family who has had to fly halfway across the world under the most horrific circumstances and we want to be able to give them some answers".
"The safety and well-being of our students and staff is of paramount importance and we are providing every possible support following this tragic incident", the spokeswoman said.
Stella Tzevakos said she was fearful that a killer was on the run in the area. "In Melbourne? It's not safe?" he asked. "You can say things like don't go out at night but why should we have to compromise our lifestyles".
"I found out yesterday evening", her classmate said.
"There is nothing we can do and it makes you feel helpless".