"The incidents were initially investigated as murders, but in light of further information received during the night, the offences include now murders with terrorist intent and their attempts," police said in a statement.
The suspect's "identity is known to the police. He is an 18-year-old Moroccan citizen," it said, providing no other details about him.
Police shot and wounded the knife-wielding suspect on Friday, arresting him minutes after an afternoon stabbing rampage at a busy market square in Turku in southwestern Finland.
Police on Saturday raised the number of injured in the attack from six to eight, adding that the injured included an Italian national and two Swedes. The other victims were all Finns.
Police also arrested five people in a Turku apartment overnight.
Two dead, eight injured in Finland stabbing spree, suspect arrested
"There was a raid and we have now six suspects in custody, the main suspect and five others," detective superintendent Markus Laine of the National Bureau of Investigation (NBI) told AFP.
"We are investigating the role of these five other people but we are not sure yet if they had anything to do with (the attack)... We will interrogate them, after that we can tell you more. But they had been in contact with the main suspect," Laine said.
In June, Finland's intelligence and security agency Supo raised the country's terror threat level by a notch, from "low" to "elevated", the second notch on a four-tier scale.
It said at the time it saw an increased risk of an attack committed by the the so-called Islamic State (IS) group.
Knife attacker in Russian city wounds 8, shot by police
Police have said they are collaborating with the Finnish Immigration Service and international authorities in their investigation.
"Several national authorities are participating in the investigation. We are also working together with our foreign colleagues to investigate the case," it said in a tweet.
The suspect is being treated in hospital in intensive care for a gunshot wound to the thigh.
The motive for the attack was not yet known.
"We haven't yet interrogated the main suspect because of his medical condition," Laine said.
Police also said they had impounded a white Fiat Ducato van suspected of being tied to Friday's stabbing, but provided no other information about how it was linked.
On Saturday, the interior ministry ordered flags to fly at half-mast across Finland in honour of the victims.
The Nordic country also raised its emergency readiness nationwide after the stabbing, increasing security at airports and train stations and putting more officers on the streets.
Media reports in Finland said police believed the suspect had picked his victims at random, but Laine could not confirm that.
Police have said it was likely the suspect acted alone, but said Friday they were looking for "other possible perpetrators."
In Turku, Finnish President Sauli Niinisto attended a vigil held in the Turku Cathedral on Friday evening in honour of the victims.
COMMENTS
Comments are moderated and generally will be posted if they are on-topic and not abusive.
For more information, please see our Comments FAQ