The shooting has shocked Finland, where gun crime is unusual
Under the plan, minors would be banned from buying guns but would be allowed to use them under adult supervision.
Currently, 15-year-olds can buy guns with parental permission. Finland has the world's third highest rate of gun ownership according to a recent survey.
A student, 18, killed eight people and fatally wounded himself at his school in the town of Tuusula on Wednesday.
The shooting shocked Finland, which has low levels of violent crime despite the high rate of gun ownership.
According to the Small Arms Survey, based in Geneva, Switzerland, only the US and Yemen have more firearms per capita.
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Hunting and shooting are popular in Finland and the country has until now resisted pressure to bring its gun laws into line with the rest of Europe.
"The cabinet is ready to agree on a proposal which says that those under 18 years old can use a gun only under parental or adult guidance," said cabinet spokeswoman Sanna Kangasharju.
FINLAND GUN FACTS 5.2 million population World's 3rd highest gun ownership 56 guns per 100 people Low rate of gun violence Guns used in 14% of homicides
In pictures: Finland shooting Finland shocked at shooting
Pekka-Eric Auvinen opened fire in Jokela High School with his .22 calibre pistol on Wednesday as students were about to start their lunch break.
Six students and two members of staff, including the female head teacher, were killed before Auvinen shot himself in the head.
He was taken to hospital with critical injuries and died later.
Police have found a suicide note he left where he explained his hatred towards society, police said.
He also gave a warning of the shooting in a video posted on the internet.
Police said Auvinen had apparently selected his victims at random but had been intent on causing maximum damage.
Auvinen obtained the licence for his pistol on 19 October, police said.
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Finland is considering toughening gun legislation in light of this week's Jokela school shooting. Nine people, including the gunman, were killed when Pekka-Eric Auvinen, 18, went on a shooting spree at his local school.

Until now, Finland has actively resisted plans for all European Union member states to limit gun ownership to persons aged 18 and over. Currently, the law stipulates that Finns may apply for a gun permit at age 15.

However, Anne Holmlund, Finnish interior minister, told reporters today that "Finland has changed its position to the EU firearms directive." Holmlund told the press that the intention is now to raise the age for ownership to 18, and require those aged 15-18 to be under parental supervision when carrying or using a firearm.

Prime minister of Finland Matti Vanhanen had earlier commented that the shooting would likely cause a change in Finnish gun control policy, but Holmlund denied a direct connection. "There is no direct link (to the school shooting). ... It is important that our new position is clear," Holmlund said.

"We were the only EU member country that was willing to keep its regulations untouched and it was obvious we would be left alone." She added.

"As all other EU countries are ready to accept the age limit of 18 years for the acquisition of firearms ... Finland does not want to oppose the said amendment to the directive under the circumstances."

"The cabinet is ready to agree on a proposal which says that those under 18 years old can use a gun only under parental or adult guidance," commented cabinet spokeswoman Sanna Kangasharju.

Ministry spokesman Ilkka Salmi agreed that a potential change in legislation was being considered months beforehand, but added that, "It's obvious that this kind of tragic incident has probably sped up the decision."

Auvinen had obtained a license for his .22 caliber handgun via a local shooting club just weeks prior to the attack, on October 19. He opened fire on students and staff shortly before lunch break was due to start, killing five students and two staff members with the gun, which he called 'Catherine' in internet discussions, before turning it on himself. He later died in hospital. There is also evidence he attempted to set the building on fire.

Police have commented that he had apparently acted with intent to kill as many as possible, but selected his victims at random. The day prior to the incident, he posted a video on YouTube announcing his intentions. Police have also recovered a suicide note that said that he hated society.

In related news, police are investigating after an internet posting claimed Kirkkoharju middle school in Kirkkonummi was going to be the subject of another attack. Police say they are treating the incident as a "bad joke".

Finnish gun ownership per capita is the third highest in the world, due largely to a long tradition of hunting sports in the country, but fatal attacks are exceedingly rare. Around 13% of the 5.2 million inhabitants own a gun, with only the United States and Yemen having higher levels of gun ownership.