Saari, a culinary arts student, was dressed in black and wearing a ski mask when he marched into his school and shot dead eight female students, one male classmate and a male teacher trapped inside a classroom.
He then set several fires in the building before turning his gun on himself.
Before his shooting rampage, Saari had posted a number of video clips on YouTube showing him shooting his semi-automatic .22 calibre handgun.
He had left behind two notes saying he "hated mankind and the human race", and "I want to murder as many people as possible", according to police.
There are several similarities with the November 7, 2007 attack carried out by Pekka-Eric Auvinen. The 18-year-old shot six students, a headmistress and a nurse before killing himself in a school in Jokela, north of Helsinki.
Before that attack, Auvinen had posted a video entitled "Jokela high school massacre - 11/7/2007" on YouTube, showing him in a T-shirt stating "Humanity is overrated."
Saari traveled more than 300km from Kauhajoki to buy his gun from a firearms dealer in Jokela, Neulaniemi said.
The investigator would not confirm his gun had been bought from the same Jokela store where Auvinen had purchased his .22-calibre weapon, but the small town only has one gun shop.
|An aerial view of the school, which has about 200 students [AFP]
While investigators have yet to reveal evidence the two young men met in person or had phone or computer contact, they say they believe the contents of Saari's computer could help establish the link.
"Our priority is to identify the victims and to try and understand the reasons for the shooting and the fires," Neulaniemi said.
"We're interviewing pupils and staff from the school. Then we'll interview any person who knows about Saari's background, and investigate his computer," he said.
Around 30 people have already given police statements, he added.
Also on Thursday, police detained at least five people around Finland for issuing threats or suspicious messages.
Police said they were taking a hard line on people making threats in the aftermath of the Kauhajoki school shooting.
Even pranksters could face prosecution, Urpo Lintula, a police spokesman, said. "The text messages are threatening in nature and are causing fear and hysteria among young people, and we must stop them.''
Finnish media said several schools across the nation had received bomb threats, and that one school had been evacuated.