Two other Viertola school students, also aged 12, were severely injured in Tuesday's attack, hospital officials and police have said.

There was no update on their medical status early on Wednesday and police were not immediately available for comment.

After word spread of the shooting on Tuesday morning, anxious parents waited for hours outside the school as teachers kept classroom doors shut to protect their pupils while police officers searched the premises.

A suspect in the case was eventually apprehended some 4km away while still in possession of a gun.

There were no other suspects, police said.

They did not identify the alleged shooter or victims, apart from saying they were all 12-year-old pupils at the school and that the suspect was a boy.

One of the injured children was a girl from Kosovo, the Kosovar foreign ministry said in a post on Facebook.

The government asked Finns to join in a day of mourning on Wednesday and ordered that the flags at public buildings be flown at half mast in a symbol of respect for the dead child.

Police have yet to say anything about the motive.

The handgun's permit belonged to a relative of the suspect, they said.

Following deadly school shootings in 2007 and 2008, Finland tightened its gun legislation in 2010 and introduced an aptitude test for all firearms licence applicants.

The minimum age for applicants was also raised to 20 from 18.

There are more than 1.5 million licensed firearms and about 430,000 licence holders in the country of 5.6 million people, where hunting and target shooting are popular.

Australian Associated Press