Putin asked that the investigation be carried out in a professional and objective manner, without any political bias, adding that Russia is interested in finding out who was the real perpetrator.
At the meeting, Bastrykin Alexander, Chairman of the Investigative Committee of Russia, said 2 more people have died at the hospital, bringing the fatality count to 139, with 182 others injured.
On Monday Russia arrested a number of people believed to have been involved in the crime.
Kremlin spokesperson Dmitry Peskov said international cooperation is necessary in the fight against terrorism, but dialogue is currently paused due to global tensions. Peskov noted that Russia's special services are working independently on investigating the terrorist attack.
French President Emmanuel Macron told reporters on Monday after arriving in French Guiana that a branch of the Islamic State carried out the March 22 attack.
That particular group made several attempts to carry out attacks on French territory, said Macron, adding that Paris has offered to cooperate with Russian security services and there will be some collaboration on a "technical and ministerial level".