Danish-born Omar Abdel Hamid El-Hussein, 22, was killed after opening fire on officers who had closed down the area surrounding Norrebro metro station.
El-Hussein had two handguns on him when he was killed and the police search later found an automatic weapon that may have been used in the attacks.
Jens Madsen, head of the Danish intelligence agency PET, said the gunman was known to intelligence services prior to the shooting and probably acted alone. PET is working on a theory that the perpetrator could have been inspired by the events in Paris.
Police said he had a record of violence, gang-related activities and weapons possession
Two civilians – a synagogue guard and a film-maker – were killed and five police were wounded in the two separate attacks in the Danish capital on Saturday.