Prime Minister Malcolm Turnbull said there was no definitive proof the man who drove a car into a crowd of pedestrians in inner Melbourne was a politically motivated terrorist.
Mr Turnbull said while the arrested suspect told police he was motivated partly by the "mistreatment of Muslims", he said police were not confident in describing the attack as terrorism.
The comments were made from the hospital where the suspect - an Australian citizen of Afghan descent - also told police he was experiencing "dreams and voices". Police have not yet conducted a formal interview.
The prime minister said he had been in constant contact with the Victorian premier Daniel Andrews, Home Affairs minister Peter Dutton and the various national security agencies.
Mr Turnbull said he was not being "circumspect" about calling the attack terrorism.
He said it was not his job to "jump to conclusions" and said labelling the attack as terrorism was a job for the police.
"To be attacked like this, in the middle of one of our great cities, is a shocking event, a shocking crime," Mr Turnbull said in a press conference on Friday morning.
He said a "mass of material" was being investigated by police and stressed no motivation "should be ruled out".
There had been 19 people admitted to hospital, he said, with three now on the critical list. Nine of the victims were foreign nationals.
