(AP) -- A homemade explosive device brought down a Russian passenger plane over Egypt last month, the head of Russia's FSB security service said Tuesday, telling Russian President Vladimir Putin it's now clear the bombing that killed 224 people was a "terrorist" act.

The Islamic State group has claimed responsibility for downing the Russian plane in written statements, as well as video and audio messages posted on the Internet following the crash.

"According to our experts, a homemade explosive device equivalent to 1 kilogram of TNT went off onboard, which caused the plane to break up in the air, which explains why the fuselage was scattered over such a large territory. I can certainly say that this was a terrorist act," FSB head Alexander Bortnikov said.

He said tests showed the explosives had been produced outside of Russia, but gave no further details.

All of the people on board, most of them Russian tourists, were killed when the plane crashed shortly after taking off from Sharm al-Sheikh on Oct. 31.

Putin vowed to hunt down those responsible for the attack.

"There's no statute of limitations for this, we need to know all of their names," Putin said. "We're going to look for them everywhere wherever they are hiding. We will find them in any place on Earth and punish them."

The Islamic State said the attack was retaliation for Russia's air campaign against IS and other groups in Syria, where Moscow wants to preserve the rule of President Bashar Assad.

Putin said Tuesday that Russia's air campaign in Syria "should not only be continued but should be intensified so that the criminals realize that retribution is inevitable."

He instructed the Defense Ministry and General Staff to present their suggestions on how Russia's operation in Syria could be modified.

"In this work, including the search to find and punish the criminals, we are relying on all of our friends," Putin said. "We will act in accordance with the U.N. Charter's Article 51, which gives each country the right to self-defense. Everyone who tries to aid the criminals should understand that they will be responsible for giving them shelter."

The Islamic State group has warned Putin that it would also target him "at home," but did not offer any details to back its claim. While releasing specifics would add credibility, the group may be withholding because its claim is false, because doing so would undermine plans for similar attacks in the future, or because the aura of mystery might deepen its mystique among die-hard followers.

IS has also claimed responsibility for Friday attacks in Paris that killed 129 people and wounded 350 others.

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Nataliya Vasilyeva in Moscow contributed to this story.