The suspect "asked at least one person if they were Muslim before he assaulted them," Blair Anderson, the police chief in the city of St Cloud where the attack took place, told journalists.
But he emphasized that the assailant's motivation remained unclear and said "whether that was a terrorist attack or not, I'm not willing to say that right now because we just don't know."
The attack came as 29 people were injured in a deliberate explosion in a busy New York neighborhood Saturday. Mayor Bill de Blasio said there was no known link to terror at this stage.
The lone suspect was wearing a private security uniform and had at least one knife, and "made some references to Allah," the police chief said.
"That suspect was confronted by an off-duty police officer and summarily shot and killed," he said.
Anderson said the eight people injured were taken to a hospital, where one is expected to remain.
The suspect had a history of minor traffic violations, Anderson said, adding that police do not currently have reason to believe the attack was connected to any other incident.
The St Cloud mall was put on lockdown in the aftermath of the attack, with local media reporting that people were being allowed to leave late Saturday. The facility will remain closed as police continue their investigation.
"It's an awful day," Anderson said. "Starting tomorrow things won't be the same here.
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