A staunch USA ally, Australia has been on alert for such violence after a Sydney cafe siege in 2014, and its intelligence agencies have stepped up scrutiny, though Ashton said there was no warning of the latest attack.
Officers were confronted near the burning auto by a man "brandishing a knife and threatening them" while passers-by called out that people had been stabbed, Victoria state police Superintendent David Clayton said.
Friday's attack began just before the evening rush hour and lasted only minutes.
Victoria state Police Commissioner Graham Ashton said Shire Ali, who was shot by police and died in a hospital, was known to police and the federal intelligence authority ASIO.
Police said that there was no known link to terrorism at this stage and that "we'll keep an open mind as to whether there's any link".
Police said the Muslim brothers were from a Somalian family that moved to Australia in the 1990s.
After Khalif emerged from the vehicle, he then stabbed three men - one fatally - before his quest for martyrdom ended with police bullets.
Shire Ali died in hospital after being shot by a rookie police constable who was just three months out of the academy.
Victoria Police said officers "initially responded to a report of a vehicle on fire" in the city center at around 4:20pm local time, as people began to leave work for the weekend.
The deceased suspect had stabbed three people, leaving one dead and two others injured but they are not believed to be life-threatening wounds. In a statement, Australian Prime Minister Scott Morrison said he condemned the act of terrorism in Melbourne, describing it as an "evil and cowardly attack".
Dubbed Trolley Man by the internet, the unidentified man used a shopping trolley to repeatedly ram the knife-wielding attacker, who was slashing at police.
The group's Amaq news website provided no evidence for the claim.
Australia has been on heightened alert from 2015 for attacks by home-grown militants returning from fighting in the Middle East.
The two other victims were in hospital, with local newspaper The Age reporting that one has a head injury and the other a neck injury.
The ute bursting into flames on Bourke Street.
Initial police investigations into Friday's Melbourne terror attack show the offender, Hassan Khalif Shire Ali, failed to complete his proposed mission.
Victoria's Premier Daniel Andrews praised members of the public for stepping in.
Bourke Street Mall, a pedestrian strip and shopping area popular with foreign tourists including Japanese, was previously the scene of vehicle rampage in 2017 that left six people dead.