Earlier in the day, Kremlin spokesman Dmitry Peskov said that Putin and Pezeshkian held a telephone conversation.
"The mutual commitment to further strengthening the Russian-Iranian strategic partnership was confirmed," the Kremlin said in a statement.
The presidents also confirmed their commitment to implementing joint economic projects in various areas, the Kremlin added.
"During the telephone conversation, President of the Islamic Republic of Iran Masoud Pezeshkian informed President of the Russian Federation Vladimir Putin of the Iranian leadership's active efforts to normalize the situation in the country," the statement read.
Moscow and Tehran advocate for a swift deescalation of tensions around Iran and for resolving problems through diplomacy, the statement added.