"The female has sustained injuries that are likely to have been caused by a sharp weapon which has not been located," he said.
"We would encourage anyone living in the area to check their homes for any unusual items or property that maybe found and contact Counties Manukau Police urgently if anything is located."
Police said a team of 25 officers working on the investigation and a post-mortem is still being conducted.
The house was cordoned off yesterday and police had spoken to neighbours. An officer at the scene told the Herald no one, including Alicia's family, had heard anything from the sleepout overnight.
Police were speaking with Alicia's family, including her father Peter and brother John, and her former partner Karl Eddy, as part of the investigation.
Mr Eddy changed his Facebook status to "single" on Tuesday, then wrote: "Why do most women all ways do this to me i work hard trust a women neva hit a women i run around after them but still not gud enuf even after my kids got atach to her as well."
Mr Gutry said yesterday the people spoken to by police were not considered suspects.
They were speaking to officers as part of the investigation to try to piece together Alicia's last hours. He said speaking to those close to her, and reviewing Mr Eddy's Facebook post, was part of the investigation.
He said she lived in the sleepout alone but could not say whether there were any signs of forced entry.
"Her death at this stage is suspicious. We're in the very early stages at the moment," he said.
"We are still working through the scene examination. Her family is distraught and they are making statements to police."
No weapons or unusual items were found at the scene.
One woman, who has known the McCallion family since they moved to Cotton Place about 20 years ago, was shocked when police knocked on her door and told her what had happened.
"There was nothing happening around here in the lead-up to this," she said. "They are a normal family, lovely."
Alicia grew up in Papakura, attending Opaheke School and Rosehill College.
- APNZ with nzherald.co.nz