The 35-year-old Eritrean suspect attended a meeting on his asylum status just hours before the knife attack, officials added.
The suspect, who was found at the scene with serious knife injuries, had earlier met to discuss his failed residency application, the Swedish Migration Agency said.
A mother and her adult son died in the attack in Vasteras on August 10.
A second man has also been detained.
On August 12, the prosecutor’s office said that investigators were still holding the 23-year-old who was staying at the same centre for asylum seekers as the injured man.
He has denied any involvement in the attack.
Police say the reason for the stabbing is unclear, but they do not believe it was politically motivated.
Migration officials said the 35-year-old had attended a meeting at the agency on Monday morning about plans to deport him to Italy after his residency application was rejected last month.
Swedish newspaper Aftonbladet has reported that CCTV images show the suspect grabbing two knives from the kitchenware section of IKEA just before the two shoppers, a 55-year-old woman and her 27-year-old son, were attacked.
“The attack ends when the alleged murderer stabs himself in the stomach,” the report said.
Police chiefs have not confirmed the footage or whether knives on sale in the shop were used.
The 35-year-old has not yet been interviewed due to the serious nature of his injuries.
Police increased security at refugee accommodation centers in the region this week after confirming they had arrested two Eritrean asylum seekers over the murders.
The store in Vasteras, which is about 70 miles west of the capital Stockholm, is one of the largest in Sweden.
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