The seesaw fight for Aleppo, once considered an al-Assad stronghold, has continued nearly unabated since July, though the number of casualties has steadily increased.
"Those behind the attacks and those who carried them out must be found and punished," the Foreign Ministry said in a post on its official Twitter account. "Supporting those who commit crimes like these is immoral and inadmissible."
Russia, along with China, has repeatedly blocked U.N. Security Council efforts to try to end the carnage. Russia's Foreign Ministry has said the conflict must be decided by the Syrian people.
While most of the Western members of the Security Council condemned the border attack, Lavrov, the Russian foreign minister, had sharp words for the council's failure to condemn the attack in Aleppo.
He said he regrets the "Security Council once again failed to condemn terror acts in Syria."
Lavrov also said Damascus should promise publicly to prevent armed incidents on the border with Turkey.