A still from a video of the suspect firing a gun was released on YouTube
Finland's prime minister has called for gun laws to be tightened after a school shooting that left 11 people dead.
Matti Vanhanen said Finland should consider banning private handguns.
On Tuesday Matti Juhani Saari shot nine students and a teacher at a college in the western town of Kauhajoki, before turning his gun on himself.
He had been questioned by police a day earlier after posting on the internet a video clip of himself at a shooting range, but was not detained.
An investigation will now be launched into police actions prior to the shootings, prosecutors say.
Flags are flying at half-mast across Finland in a day of national mourning for the victims of the shooting.
In Kauhajoki, grieving residents placed candles and flowers outside the college as police started lifting some of the cordons.
Mr Vanhanen visited the town to offer support to a small quiet community, shell-shocked by what had happened.
"We have to tighten the law significantly," the prime minister said.
"In terms of handguns that can easily be carried about, we have to think about whether they should be available for private people. In my opinion, they belong on shooting ranges."
Tuusula, Finland, November 2007 - nine dead, including gunman
Virginia Tech, US, April 2007 - 33 dead, including gunman
Erfurt, Germany, April 2002 - 18 dead, including gunman
Columbine school, Denver, US, April 1999 - 15 dead including two gunmen
Dunblane, Scotland, March 1996 - 16 children, one teacher and gunman dead
Tuesday's shooting echoed another in November last year in the town of Tuusula, which left eight people and the lone gunman dead.
Both gunmen had valid licences.
Although Finland said it would consider new laws after that attack, no changes have been made and 15-year-olds can still own guns.
The country has a long tradition of hunting and weapons-bearing. An international small arms survey in 2007 showed an averaged total of 2.9 million firearms within a population of 5.2 million people.
Mr Vanhanen said: "The question is what kind of guns should be available with a licence. After these incidents, we have to discuss whether handguns should be legal."
Questions will also be raised about the police handling of the case and the role of the internet.
Saari, 22, was questioned on Monday but police said the videos "did not threaten anyone" directly.
Mr Vanhanen said authorities would also look at whether there needed to be changes in internet monitoring.
He said: "The internet and YouTube forums... are not another planet. This is part of our world and we adults have the responsibility to check what is happening, and create borders and safety there."
Saari posted several videos. One, which emerged on Tuesday, showed him saying to the camera "you will die next", followed by three gun shots.
Police said they had found a note in Saari's flat explaining his actions.
The head of the police investigation, Jari Neulaniemi, said: "In the note he said he hated mankind and the human race. And that he had been planning this since 2002."
The attack in Kauhajoki, some 330km (205 miles) north of the capital, Helsinki, started just before 1100 local time (0800 GMT).
Mr Neulaniemi said nine victims had been found in one classroom. Another was discovered injured in a corridor and later died in hospital.
Eight of the dead were female students, investigators said. All 10 victims also had severe burns because the attacker set fire to the classroom. Another female student was seriously wounded.
Saari shot himself in the head and later died in hospital.
Saari, dressed in black and wearing a ski mask, was seen entering the building with a large bag.
School caretaker Jukka Forsberg told AFP news agency that two girls had told him a man was shooting.
"I saw a guy leaving a big black bag in the corridor and going into classroom number three and closing the door," he said.
"I looked through the window and he immediately shot at me... Thank God I was not hit, he fired at me but I was running zigzag. I ran for my life."