Anna Bergkvist, the head of the police investigation, told the BBC that police could confirm only that people of multiple nationalities and ages were caught up in the attack.
Salim Iskef, a 29-year-old Orthodox Christian who fled the war in Syria in 2015, has been named as one of the 10 victims of the shooting.
Santa Maria church in Orebro said his life had ended tragically in the attack. Swedish reports said he had become a Swedish citizen and was due to get married in June.
His aunt told Arabic-language website Alkompis that he had made a video-call to his mother to say he had been shot and asked her to look after his fiancée.
Two Bosnian citizens are also among the victims, Bosnia’s ambassador has told Swedish daily Expressen. One was wounded and another was missing, he said. The Bosnian foreign ministry has expressed its condolences and spoken of Orebro’s large Bosnian community.
Police in Orebro said the alarm was raised at 12:33 (11:33 GMT) on Tuesday and after about five minutes the first patrols had reached the school, which sits on a large education campus about 200km (124km) west of Stockholm.
Regional police chief Lars Wiren told a news conference on Thursday that 130 police officers eventually reached the school.
They faced what could only be described as an “inferno” when they entered the school buildings on Tuesday, he said: “Dead people, screams and smoke.”
He spoke of a scene of chaos, with people running inside and outside a very large school that stretches out over about 17,000 sq m.
Wiren told the BBC that there was no evidence bombs had been detonated, but said there was thick smoke that could have come from the suspect setting fires or smoke grenades.
He said they believed the suspect had fired at police but that officers did not fire back. The gunman was found dead at the scene over an hour later.
Police investigator Anna Bergkwist said that the suspect had killed himself.
She confirmed that three guns were found at the scene next to the gunman, of a total of four known to be legally registered to the suspect.
However, she refused to comment on the types of guns or ammunition used.