A gunman who killed 11 people, including himself, at an adult education centre in central Sweden may have been a student at the school, police said on Thursday, as they described chaotic scenes after the country's deadliest mass shooting as being like an "inferno".

Officials in Sweden have vowed to determine why a man killed 10 people, and apparently himself, in an unprecedented attack that's shaken their "society to its core."

The police responding to the attack encountered firing so intense that they struggled to tell how many gunmen were on the scene, an official said.