“What I can say is violence against any person is not, and will not, be tolerated,” she said.
McDonald said police would keep “all lines of inquiry open” but there was no suggestion from police that they were hunting anybody else.
Crime scenes were established where each of the bodies was found, and police spent Monday afternoon going in and out of the unit complex, some carrying specialised cameras and brown paper evidence bags.
A police tent was set up below balconies near the Belmore Street end of the complex. Residents in neighbouring buildings watched from their windows.
The building, which is located next to the Masonic Temple, is in the heart of Burwood’s high street shopping area.
Homicide squad detectives and officers from Burwood Police Area Command and South West Metropolitan Region will make up Strike Force Trophins, which is continuing investigations into the deaths.
Police urged anyone with information about the deaths to contact Crime Stoppers on 1800 333 000 or online at www.nsw.crimestoppers.com.au.
If you or anyone you know needs support, you can contact the National Sexual Assault, Domestic and Family Violence Counselling Service on 1800RESPECT (1800 737 732), Lifeline 131 114, or Beyond Blue 1300 224 636. The men’s referral service is on 1300 766 491.