Prime Minister Scott Morrison has deemed the murder of an international student in Melbourne the "most despicable of crimes", while Labor leader Bill Shorten says it was "shocking and senseless".
The body of Aiia Maasarwe, 21, was found in scrub not far from where she got off a tram at the northern suburb of Bundoora late on Tuesday night.
Police say the Palestinian Arab of Israeli citizenship suffered a "horrific" assault and have launched a widespread hunt for her killer.
Mr Morrison says Ms Maasarwe's murder is "just so shocking".
"I mean, I'm speechless," he told reporters in Fiji on Friday.
The prime minister said his heart goes out to Ms Maasarwe's family, though he can't begin to think of what he would say to them.
"I know what I'm thinking about her attacker. I expect it's the same thing that all other Australians are thinking today," he said.
"I know the police will do their job and they'll deal with it. But the rest of Australia has to wake up today and deal with the most despicable of crimes.
"My heartfelt condolences on behalf of Jenny and myself and my family, to her family, and I just I pray you can find whatever comfort you can in the worst of all circumstances."
The prime minister stressed every woman and person in Australia should be able to travel home safely and that the government must remain "forever vigilant" to the issue of male violence against women.
"It's a top priority order issue for our government and has been."
Mr Shorten said the murder doesn't reflect the Australia or Melbourne he grew up in.
"I want to say to parents whose young people come to Australia, this is shocking but this is not Australia," he told reporters in Brisbane on Friday.
He said his feelings for the grief of Ms Maasarwe's family are strong but he wants to reassure them Australia's police are among the best in the world.
"They will successfully catch, and our legal system will punish, the wrongdoer," he said.
Ms Maasarwe had been attending college on the grounds of La Trobe University, and visited a Melbourne comedy club before catching the tram home on the night of her death.
The event has sparked a series of vigils and renewed concerns about male violence.
