"Our state's security organs are taking the appropriate measures to ensure the security of citizens and their protection against terrorism," the National Anti-Terrorism Committee said in a statement after Friday night's unprecedented violence in the French capital.
"In light of the new threats, all components of the security system have put been put on high alert."
The statement also urged Russian citizens to exercise "high responsibility and vigilance" in the face of international terrorism.
Putin added that Russia was ready to "closely cooperate" with France in its investigation of the attacks.
In the immediate aftermath of the bloodshed, the Kremlin offered its condolences, condemning the "hateful" string of attacks and "inhuman murders".