Police said forensic testing was being conducted on two pieces of clothing found nearby that they believe was likely to have been left by the person responsible for her death.
Another of Ms Masarwe's uncles, Abed Katane, told Israeli news outlet Haaretz her family was in shock.
"This was an absolutely horrendous, horrific attack inflicted on a completely innocent young woman who was a visitor to our city", he added.
"Nothing in the victim's background indicates this was anyone known to her".
Police believe the attack was random and opportunistic.
The body was found near Polaris Town Centre, a popular shopping area.
"We would ask for anyone that may have dashcam footage, CCTV or may have seen anything here that could be a small piece in the jigsaw puzzle to contact Crimestoppers", Insp Stamper said.
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The regional court of Mannheim decided that iPhones infringe Qualcomm's patents to circuit technology and dismissed the lawsuit. A German court has thrown out a patent suit filed by U.S. chipmaker Qualcomm against Apple , in an initial verbal decision .
She had been out at a comedy show, 9News reports, and was taking a tram as she spoke on the phone with her sister.
Aiia was facetiming with her sister as she got off the tram, during which her sister heard the beginning of the brutal assault that has horrified the local population and led to increased calls for government action to protect women.
"Pretty much she heard the sound of the fall to the ground, some voices.at 10 past midnight on Wednesday night".
An unprecedented number of homicide detectives were investigating the scene on Wednesday and Thursday, with dozens of officers performing line searches in surrounding scrubland.
"I feel very, very sad from one side, but from another side, when I get this support and this help from the people, from the community, from the police, this is make the suffering at least to feel more, a little more better", Mr Maasarwe said.
"This is a very distressing matter, very distressing to the victims, the community and of course very distressing to the police", he said. "I had many dreams to be with her".
The cap is black in colour and has "1986" printed on the front.
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Detective Inspector Stamper said he was confident the offender would be caught quickly.
"I don't know how long time I need to wait".
A tram carrying only flowers will depart from there following the route of her final journey later Friday.
The family alerted police at around the same time that Ms Maasarwe's body was found at 7am on Wednesday near the tram stop.
Main Drive has been cordoned off by police.
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. He said "every available resource" was being poured into the investigation.
Aiia Maasarwe's father has arrived to identify the body, which the Israeli embassy said it would assist with returning to Israel.
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