Police are still trying to confirm whether or not Andersson acted alone, prosecutor Elisabeth Andersson told the Expressen tabloid.
On Sunday police said they were still struggling to establish Andersson's motive, five days after the tragedy.
He killed 10 people on February 4th after entering the Campus Risbergska, an educational centre for adults in the town of Örebro, 200 kilometres west of Stockholm, before apparently turning the gun on himself.
While police confirmed the gunman was a former student at Risbergska, Örebro police commander Henrik Dahlström acknowledged that what had sparked the killing spree was still unknown.
"We cannot for the moment establish that a clear motive exists," Dahlström told journalists on Sunday.
"We are working to see if there is one and what it might be."
Andersson was a 35-year-old unemployed recluse with psychological problems, Swedish media reported.
"Sweden is a country in mourning," Prime Minister Ulf Kristersson said in a televised address on Sunday.
"At this moment, we are being put to the test. Each in our own way, but also as a country."
The attack had provoked fear and concern among the population, he added.
'Not us and them'
Dahlström said that had it not been for the swift intervention of the police, the toll could have been higher.
Police have previously said they faced "an inferno" when officers arrived at the scene of the killing spree.
Officers found three weapons found next to the suspect's body, along with "a great deal of shell casings" and unused ammunition.
Andersson killed seven women and three men aged between 28 and 68. All lived in Örebro but were of "multiple nationalities", investigators have confirmed.
"They came from different parts of the world and had different dreams," Kristersson said.
"They were at school to lay the foundations for a future that has now been taken away from them."
Syria's embassy in Stockholm has expressed condolences to two Syrian families, without giving details.
Bosnia's foreign ministry said one of its nationals was among the dead, while another had been wounded.
Kristersson, who urged people not to speculate on the attacker's motives, stressed that he understood the concerns of "people of foreign origin who show a particular sense of vulnerability".
However, "there is only one Sweden. Not us and them. Not young or old. Not born here or born abroad", he added.
Kristersson's government is backed by the far-right on the basis of a programme calling for a sharp reduction in immigration.
SVT public broadcaster analyst Mats Knutson said "if it turns out that racist motives were behind this murder, it will trigger a very lively debate on the change of tone and rhetoric in Swedish political debate, particularly on the issue of immigration".
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