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Investigators have determined that the suspect is a Moroccan man born in 1994.
"The police have interviewed the main suspect, and he is willing to communicate with the interviewing police officer," the National Bureau of Investigation said in a statement, adding that it would not release details of his statements while the investigation continues.
But the police now say the man's name is not Abderrahman Mechkah, as he was previously identified.
"He gave false information to the Finnish authorities when he arrived in Finland" and requested asylum, Detective Inspector Crista Granroth, who is leading the NBI's investigation, told AFP.
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Police have said that the man targeted women in a rampage on August 18 at a market square in the southwestern port city of Turku.
Two women were killed and eight people were wounded: six women and two men who tried to fend off the attacker.
Reports in the Finnish media also say that while the man has acknowledged making the attacks, he said he had not intended to kill anyone and denied any terror motive.
Six other people have been arrested on suspicions of being involved in the attack, though three of them have since been released.
Two of the men released were a Moroccan national and an Algerian detained on Wednesday.
Investigators are treating it as the country's first terror attack.