The shooting took place on Tuesday at the Campus Risbergska, an educational centre for young adults in the town of Örebro, 200 kilometres (125 miles) west of Stockholm.
All of the victims, aged between 28 and 68 years old, lived in Örebro, police said in a statement.
Law enforcement did not share any details on the victims' nationalities.
READ ALSO: 'Multiple nationalities' among victims in Swedish mass shooting
Victims are of "different nationalities, different genders and ages," Anna Bergqvist, who is heading the investigation, had told AFP on Thursday.
The Syrian embassy in Stockholm expressed its condolences to two Syrian victims' families, without giving further details.
A national of Bosnia and Herzegovina was killed and another was injured, the Bosnian Foreign Ministry said, citing information shared by Orebro residents.
Police have not yet revealed the name of the suspect, whose body was also found. He is believed to have killed himself.
Swedish media have identified him as 35-year-old Rickard Andersson, who had reportedly been living as an unemployed recluse and was suffering from psychological problems.
The shooter's motive remains unknown.
READ ALSO: What do we know about a possible motive for the Örebro shooting?
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