Earlier, a witness said an employee of a grocery store at the shopping centre, in Espoo town, was left lying on the floor after the gunman opened fire.
The police have surrounded the mall but the gunman remains at large, a spokesman told the Finnish MTV3 TV channel.The Ilta-Sanomat newspaper’s website said at least seven shots had been fired, but gave no source for that information.
Several ambulances rushed to the scene and parts of the shopping centre were evacuated.
In the past two years, Finland has seen two school shootings in which a total of 20 people died.
In September 2008, Matti Juhani Saari, a 22-year old trainee chef, shot and killed ten students who were sitting an exam at a technical school.He died of self-inflicted head wounds in hospital a few hours later.
That incident came less than a year after Pekka-Eric Auvinen — described by police as a bullied 18-year-old — opened fire at his high school, in the town of Jokela. Auvinen killed six students, a school nurse and the head teacher before turning the gun on himself.
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