"He was known as an Islamist but not a jihadist," said Andy Grote, noting "there are indications of radicalisation".
He added that while there could have been an Islamist motive for the attack, the suspect also suffered from psychological problems.
"It remains unclear which was the overriding element," said Grote.
Police piecing together the assault on Friday said the man had entered the supermarket and took a kitchen knife measuring around 20 cm from shelves.
"He ripped off the packaging and then suddenly brutally attacked the 50-year-old man who later died," said police spokeswoman Kathrin Hennings.
He later wounded two other men in the supermarket before fleeing, injuring others along the way, before he was overpowered by courageous passers-by.
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