Police have cordoned off a section of the central business district in Australia's second-largest city, but are not looking for other suspects.
Social media footage showed the attacker trying several times to stab one of the officers before a second officer drew his gun and a single shot was heard.
Three men were stabbed by the suspect and one of them died at the scene.
Mr Ashton added: "From what we know of that individual we are treating this as a terrorism incident", adding that the police counter-terrorism command was working on the case as well as homicide detectives.
He died later in hospital.
After Khalif emerged from the vehicle, he then stabbed three men - one fatally - before his quest for martyrdom ended with police bullets.
Ashton said police had spoken to Shire Ali's wife. He said the attacker was someone known to police through family connections. One of his victims died at the scene while two others were wounded.
Police have also credited the "9-11" public response - so named after those on board United Airlines Flight 93 who vainly fought to take back control of the plane from terrorists - for keeping a sense of calm during Friday's attacks.
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One witness said the man was stabbed in the face and desperate efforts were made to save him.
Authorities say Australia's vigilance has helped to foil at least a dozen plots, including a plan to attack downtown Melbourne at Christmas in 2016.
Australian Prime Minister Scott Morrison said the country would be unflinching in the fight against "radical, violent. extremist Islam that opposes our very way of life".
After putting out the fire in the auto, authorities found what Ashton described as "barbecue-style" bottles of gasoline inside the vehicle, which prompted authorities to call the bomb response unit to the scene.
"Because he was on his stomach, they turned him over to see if he's alright, he was still alive", nearby KFC worker Markel Villasin told AAP.
Bourke Street also reopened on Saturday morning, and a Reuters reporter said there was an increased police presence in the area.
As investigations into the attack continue, Victorian Premier Daniel Andrews is urging people to show up en masse for Armistice Day events.
Two hostages were killed during the 17-hour Sydney cafe siege by a "lone wolf" gunman who was inspired by Islamic State militants.