The 29-year-old man allegedly uttered 'Allahu Akbar' during the stabbing attack on late Tuesday night at a backpacker hostel near Townsville in northern Queensland state, leaving a 21-year-old British woman dead and two men with severe injuries, Xinhua news agency reported.
While investigations revealed comments that could point to extremist Islamic motivations, it was not yet fully determined if the attack was terror-related, Steve Gollschewski, Deputy Commissioner of Queensland Police, said on Wednesday.
"While this information will be factored into the investigation, we are not ruling out any motivations at this stage, whether they be political or criminal," Gollschewski said.
"Investigators will also consider whether mental health or drug misuse factors are involved in this incident," he said.
The authorities have conducted 16 counter-terror operations since 2014, arresting 44 alleged home-grown terrorists.
The French national had entered Australia lawfully in March on a temporary visa, and was not on any watch lists, Gollschewski said.
"While this matter is being treated as a homicide, the Queensland Police Service will continue to work with its federal counterparts in relation to the investigation," he said.
Australian Federal Police commander Sharon Cowden said authorities are working with international law enforcement agencies.
Authorities said they are not searching for any other suspect in connection to the attack "at this time", reaffirming there is no ongoing threat from the incident.
"This is not about race or religion. It is individual criminal behaviour," Gollschewski added.
Australia has been on high alert for terror attacks since September 2014, suffering several attacks including the lone wolf-style murder of Police accountant Curtis Cheng at a Western Sydney police station in 2015.
