Finnish police have arrested two more suspects after last week's stabbing spree, which killed two women and wounded another eight.
Police had already detained the main suspect, a Moroccan asylum seeker, and three other Moroccan men in connection with the killings on Friday. An international arrest warrant has been issued for a fifth.
The incident has been treated as Finland's first suspected Islamist militant attack.
According to the National Bureau of Investigation, the two new suspects gave different stories to Finnish and Swedish authorities - telling the former they were from Algeria and the latter they were Moroccan.
The main suspect has been named as 18-year-old Moroccan Abderrahman Mechkah, who told a court he was responsible for the attack but denied a terrorist motive.
Police said his identity is likely to be false.
"We have reasons to suspect that he has given wrong information to authorities when coming to the country," Detective Superintendent Markus Laine of the National Bureau of Investigation told Reuters.
The man identified as Mechkah arrived in Finland in 2016, lived in a reception centre in Turku and was denied asylum before the attack.
He had earlier spent time in Germany, according to authorities. German media reported on Tuesday that he had used several false identities in the country, and that he was charged with causing bodily harm.
"We can't comment yet on his motives... he has not been willing to answer all questions," Laine said.