"He apparently has ties to (militant Islamist group) Millatu Ibrahim and sympathies for IS," police said in a statement of the 25-year-old man, referring to the Islamic State group.
Saying the man was a Danish citizen who had come to the country from Bosnia when he was four years old, police said there was "currently no evidence that (his alleged IS sympathies) has influenced the shooting incidents."
Local media named the man as Mesa Hodzic.
After fleeing the scene the man was arrested early today in a suburban area near Copenhagen's airport.
He was unable to appear in court because of gunshot injuries sustained during his arrest.
In addition to three counts of attempted murder, he faces preliminary charges of possessing a firearm and trafficking 48 kilos of cannabis, 2.7 kilos of skunk - a powerful type of marijuana - and over 1,800 joints, according to Danish news agency Ritzau.
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