Finnish Police said they believe the killing of two people in the south-western city of Turku on Friday was a terrorist attack.
They said the attacker, who was shot in the leg by police and taken into custody, was an 18-year-old Moroccan.
The two people stabbed to death were both Finnish. Eight people were also injured, among them two Swedes and one Italian.
Officers raided a flat and made a number of arrests overnight.
Police said in a statement: "The act had been investigated as murder, but during the night we received additional information which indicates that the criminal offences are now terrorist killings."
They said the identity of the 18-year-old Moroccan was known, but they have not released it.
The attack happened in the Puutori/Market Square area of Turku.
Police said the alarm was raised at 16:02 local time on Friday, when a man was reported to have attacked passers-by with a knife.
Witnesses said he then ran to a nearby square and stabbed more people before he was shot in the thigh. Police said he was arrested at 16:05.
Finland has no past experience of terrorist attacks.
Source: News Agencies, Edited by website team