"We will search for them anywhere they might hide. We will find them in any part of the world and punish them," Mr Putin told Alexander Bortnikov, Russia's security chief, late on Monday. The Kremlin released the remarks on Tuesday.
"One can say unambiguously that it was a terror act," Mr Bortnikov, the head of Federal Security Service (FSB) told Mr Putin. He cited experts to say that the plane disintegrated midair due to a bomb with the equivalent of a kilo of TNT.
In response to the attack, President Putinpledged to step up air strikes in Syria where Moscow is conducting a bombing campaign it says is targeting the Islamic State group and other "terrorist" groups.
"The combat work of our aviation in Syria must not only be continued. It must be intensified so that the criminals understand that vengeance is inevitable," Mr Putin said.
The Airbus A321M had crashed shortly after taking off from the resort of Sharm el-Sheikh on its way to the Russian city of St Petersburg, killing all 224 people on board.
The terror group ISIS, which controls swathes of Iraq and Syria and is battling the Egyptian army in the Sinai Peninsula, had earlier claimed responsibility for downing the plane. Russia had said it was waiting for the official results of an investigation into the tragedy.