
Police Chief, Niclas Hallgren, said that they had based their conclusion on what was found at the killer’s apartment and “his behaviour during the act”.
Media reports suggested that the 21-year-old attacker had far-right sympathies.
Armed with a sword and wearing a helmet and mask, he stormed a school in Trollhattan, near Gothenburg, before being shot dead by police.
He was seen posing for a photograph with students, who thought he was dressed for Halloween, before going from classroom to classroom at the Kronan school.
A teacher and 17-year-old boy died from stab wounds, while another 15-year-old male student, and a 41-year-old teacher remain in serious condition in hospital.
The attacker’s name has not yet been released by police, though they said that he was local to Trollhattan. He did not have a criminal record, police said.
Police were alerted to the attack at around 10:10am local time on Thursday and later gunned down the attacker in the hallway outside a classroom.
The Kronan school has about 400 students aged between six and 15, including many children of immigrants.
Trollhattan is an industrial town in west Sweden, located about 75km (50 miles) north of Gothenburg, the nation’s second largest city.
School attacks are rare in Sweden -with just one incident on record in the past 20 years, in which one pupil was shot dead.