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One person has been arrested, Copenhagen Head of Police Soren Thomassen told reporters at a news conference.
He described the suspect as a 22-year-old ethnic Dane.
The shooting occurred on Sunday (Monday AEST) in the vicinity of Field’s, a shopping centre in the Danish capital, police said earlier.
Social media footage showed people running through the mall and heavily armed law enforcement officers on the scene.
At least three people have been hospitalised, according to a spokesman for Rigshospitalet, Denmark’s largest hospital.
Extra staff have also been called in to deal with emergency, the spokesman said.
Thomassen said police cannot rule out the incident as terror-related, and that an extensive police investigation is ongoing throughout the country.
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