His application for residency was rejected in June past year and he was being sought by immigration officials, police said.
Apart from that, the suspect expressed radical ideas and "showed sympathies for extremist organizations, among them Islamic State", Hysing added.
Police said roughly five other people remained in police custody for questioning over the apparent terror attack, in which a hijacked delivery truck mowed down pedestrians in Stockholm last Friday, killing four people.
Many Swedes were back at work for the first time since the attack, while the department store into which the truck slammed had already reopened.
Trudeau says he and his wife are praying for a speedy recovery for the injured in Stockholm.
Police arrested the man at the wheel of a white van, media said, and placed him under arrest on suspicion of "terrorist crime (by committing) murder".
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Police said on Sunday they had brought in seven people over the apparent terrorist attack outside the department store on Friday, according to Reuters. Head of the National Police, Dan Eliasson, said that the suspect had been known to the police. Authorities haven't said how he came to reside in Sweden or how long he had lived there, but he was on their radar; though, a previous investigation into the suspect had apparently gone nowhere.
The Swedish police also confirmed that a device was found in a driver's seat of the truck, but wasn't ready to call it a bomb. There has been as yet no claim of responsibility for the Stockholm assault.
Police now say one British person, two Belgians and two Swedes were killed in the attack in a busy shopping district of the Swedish capital.
The man arrested remains officers' prime suspect for the attack, which saw a hijacked lorry plough into the front of a shop in the pedestrian thoroughfare of Drottninggatan.
"Today, all of Sweden is in mourning but we are going to get through this together", he said last Saturday.
Stockholm authorities said that ten of the injured people are still in hospital, and two of them are in intensive care.
On Sunday, several thousand people gathered at Stockholm's Sergel Square to remember the victims.