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Police in Copenhagen say one person was shot in the back and one in the arm, and the third in the stomach at the Fields shopping centre on the island of Amager.
The gunfight involved eight people in two rival groups, police said, and was reported to have taken place in an underground carpark.
Speaking to news agency Rittzau, Michael Andersen of Copenhagen police said the shooting was a result of “two groups who clashed”.
At least one man was arrested on the roof of the shopping centre after the gunfight.
“It seem two groups got in a quarrel and it culminated in the parking basement in Field’s where a still unknown number of shots were fired,” Police Communications Officer Sebastian Richelsen said.
Denmark has been in a state of high alert since the attacks on a Jewish cultural centre and synagogue in February that left two people dead.
Officers killed the gunman, Omar El-Hussein, in a shootout and have arrested three people in connection with the case.
But the force has said it is still trying to piece together the sequence of events between the two attacks.
“We are still shedding light on the perpetrator’s and accomplices’ whereabouts, and this morning’s raids should be seen in that light,” Copenhagen police said in a statement.
“We’re searching for additional leads in the case and cannot comment further because of the ongoing investigation,” it added.
The attacks shocked Denmark, which prides itself on being a safe and open society. Police have said they do not believe El-Hussein, a son of Palestinian immigrants, was part of a cell.