Wammen calls Tuesday's incident "terrible and senseless" in a written comment to the Ritzau news agency.
"My thoughts and deepest condolences go to the relatives," he continues.
On Saturday, Denmark's Foreign Minister Lars Løkke Rasmussen also spoke out about the incident.
"I am filled with sadness and anger that a young Swedish man has lost his life in Copenhagen during what should have been a peaceful World Cup event. May the guilty be judged harshly and fairly," he wrote on X.
The suspected perpetrator turned himself in to police on Friday. He denies the crime. The victim was a Swedish police officer who was on vacation.
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