The slaughter Tuesday, which killed 10 people and the gunman, was Finland's second deadly school shooting in less than a year.
Prime Minister Matti Vanhanen said it was time to consider restricting access to guns in a country that has more than 1.6 million firearms in private hands.
"We need to study if people should get access to handguns so freely," Vanhanen told reporters in Kauhajoki, 180 miles northwest of Helsinki. "I'm very, very critical about the guns and during next few months we will make a decision about it."
Interior Minister Anne Holmlund said the government was working on a proposal to restrict gun laws by giving police greater power to examine applicants' health records.
"The most important thing is that police are able to have the best possible information on the state of health of the applicant when deciding on the license," Holmlund said Wednesday.
Finland has deeply held hunting traditions and ranks - along with the United States - among the top five nations in the world when it comes to civilian gun ownership.
The government also called Wednesday for an investigation into police handling of the case. Police had questioned shooter Matti Saari, a student at the school, a day before the attack about YouTube clips that showed him firing a handgun.
"We will obviously investigate what the foundation was for the decision to let him keep his weapon," Vanhanen said.
Some of the YouTube clips appeared to have been shot by another person. Police said they would question Saari's acquaintances to find out who that was but added there was no indication that Saari had an accomplice during the shooting.
Solemnly leading his nation in a day of mourning, Vanhanen and other ministers visited Kauhajoki, a town of 14,000 people, as flags flew at half-staff. Grieving residents placed candles and flowers outside the Kauhajoki School of Hospitality.
The National Bureau of Investigation said all the female victims were students, while the two men who were killed were a teacher and a student. Saari also shot another female student in the head before shooting himself in the head.
That 21-year-old woman had two operations overnight but doctors said she was in satisfactory condition Wednesday.
Investigators said most of the victims were from the Kauhajoki area, like Saari, meaning he probably knew them.
"He really went out with the intention of killing," investigation leader Jari Neulaniemi said. "He left at home a message saying he wanted to murder as many people as possible. He tried to shoot fatal shots."
Police spokesman Urpo Lintula said Saari had acquired a permit for his weapon, a .22-caliber handgun, in August.
"With this weapon and plenty of ammunition, he came into the school yesterday morning and he also had a largish bag which apparently had flammable liquids or something to start fires," Lintula said.
Witnesses said panic erupted at the school, which offers courses in catering, tourism, nursing and home economics, as the masked gunman entered just before 11 a.m. and started firing in a classroom.
His first targets were writing an exam, reports CBS News correspondent Sheila MacVicar.
By the time police got into the building, the school was on fire, there were reports of explosives, and many students had been wounded.
Last Friday, 22-year-old Matti Saari posted videos on YouTube, practicing his aim with what the Finnish government says was his legal, and only weapon.
On Monday the local police, alerted to the Internet videos, called him in for questioning. They could find no reason to detain him, or to take his gun, MacVicar reports.
A video clip posted on the Internet by the alleged gunman showed him pointing his gun to the camera and saying "You will die next" before firing four rounds.
Tuesday's rampage bore eerie similarities to another school massacre in Finland last year in which an 18-year-old gunman killed eight people and himself.
After the earlier massacre, the government promised to raise the minimum age for buying a gun from 15 to 18, but legislation was never passed. That change would not have stopped either of the recent school shooters, who were 18 and 22 years old.