In a televised address, Putin said 11 people had been detained, including the four gunmen.
Messages of outrage, shock and support for those affected have since streamed in from around the world.
Eleven of the 15 council members voted for the resolution, but the Russia and China vetoes stopped its passage.
In the 2004 Beslan school siege, Islamist militants took more than 1,000 people, including hundreds of children, hostage.
The Israeli embassy in Washington did not immediately respond to a request for comment.
Putin vowed Wednesday to provide support for Belgorod civilians who have lost their homes and businesses.
In better times, Fadi's favourite food was chicken shawarma, a Levantine grill dish, his mother said, and he ate a lot of fruit and drank…
Gaza's health ministry has said 27 children and three adults have died so far from malnutrition.
Putin said Russia might need to create a buffer zone inside Ukraine to prevent such attacks in future.
Putin is poised to win a new six-year term that, if he completes it, would make him Russia's longest-serving leader for more than 200…