"We know that he showed interest for extremist organizations like IS", Hysing said. "The Migration Agency rejected it in June 2016 and also decided that he was to be deported", Hysing said.
A woman and an 11-year-old girl from Sweden were killed in the attack, as well as a 41-year-old Briton who worked for Spotify and a Belgian woman.
Police said they were investigating the second suspect for a "terrorist crime [by committing] murder".
"I can confirm that a second person has been arrested", Stockholm district court judge Helga Hullman said.
As details emerge about what may have inspired the deadly attack that left four people dead and more than a dozen injured, investigators are scouring the suspect's mobile phone and social media accounts.
Prosecutors and police officials did not identify the suspect, but Anders Thornberg, head of the Swedish Security Service, said at a news conference that the man had been on authorities' radar some time ago.
A failed suicide bombing in December 2010 killed an attacker only a few hundred yards from the site of Friday's incident.
Eliasson said there were "clear similarities" to an attack last month in London in which six people died, including the assailant who drove a hired vehicle into pedestrians on a bridge.
The 39-year-old Uzbek man is suspected of having driven a truck into a department store in the city on Friday.
The man accused of driving the truck down the busy thoroughfare and into a major department store was arrested shortly after the attack.
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He said: "She was clear that the United Kingdom stands firmly by Sweden's side, and they agreed on the importance of working together to tackle these threats, which we all continue to face", he said.
"We received intelligence past year, but we did not see any links to extremist circles", Sapo security police chief Anders Thornberg said.
In neighboring Norway early on Sunday, police set off a controlled explosion of a "bomb-like device" in central Oslo and took a suspect into custody. Police revealed Sunday that the man applied for residence in Sweden in 2014.
Fifteen people were treated in hospitals for injuries they suffered in the attack. It said two were in intensive care, four were seriously injured but the one child was not seriously hurt. There has been as yet no claim of responsibility for the Stockholm assault.
In the meantime, police are still on guard in Stockholm and parts of the capital city remain closed to the public.
"Maybe something good will come of this", Inger Morstedt, 75, told AFP, expressing hope that her fellow Swedes would become "even more open and welcoming".
Government offices were flying flags at half-staff to honor the victims.
Prime Minister Stefan Lofven declared Monday a national day of mourning, with a minute of silence at noon. We are supporting his family in Sweden and in the UK.
King Carl XVI Gustaf, who returned to Stockholm on Saturday after cutting short a visit to Brazil, also addressed the nation outside the palace. He said the suspect was not on any current list of people being monitored.