Prime Minister Ulf Kristersson described Tuesday's attack at Risbergska school in Orebro, 200km (124 miles) west of the capital city Stockholm, as the "worst mass shooting in Swedish history", AzVision.az reports, citing BBC.
Police said they believe the male perpetrator to be among the dead and that he was not previously known to them. There was no immediately identifiable motive and he was believed to be acting alone, they said.
"It is difficult to take in the magnitude of what has happened today," Kristersson said at an evening news conference.
Police earlier warned the death toll could continue to rise as several people had been injured.
A number of the injured have been taken to hospital, with at least four people undergoing operations.
Police initially said five people had been shot, and the incident was being investigated as an attempted murder, arson and an aggravated weapons offence.
Local media later began reporting that several people had died, before police said "around 10" people had been killed but they "could not be more specific" about the number of fatalities.
They also confirmed there did not appear to be a "terror" motive behind the attack.
Police heard reports of a shooting taking place at Risbergska school - an adult education centre - at 12:33 local time (11:44 GMT). The facility sits on a campus that is home to other schools.
These centres are attended primarily by people who have not finished primary or secondary school.
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