Umakhanov made the remarks in a meeting with Iranian Ambassador to Russia Kazem Jalali.
Referring to recent developments in the Middle East, he said Russia is seriously interested in Iran's stability and promotion.
He added that Russia will do its best to reinforce and support Iran's stances in the international arena.
Meanwhile, Jalali pointed to Iran-Russian relations and called for developing political, economic, cultural and provincial ties through parliamentary cooperation.
Meanwhile, in a separate meeting with Jalali, Chairman of the State Duma Committee on International Affairs Leonid Slutsky slammed assassination of the IRGC Quds Force Commander Lieutenant General Qasem Soleimani.
He also sympathized with Iranians over the deadly Ukrainian plane crash in Tehran.
Slutsky praised the Iranian Armed Forces' brave act to accept the responsibility of the unintentional human error to target passenger plane.
After the US increased tensions in the Middle East by assassinating Iran's Lieutenant-General Qasem Soeimani, the country made a reaction and hit the US airbase in Iraq with missiles.
Iran's military had been put on alert to counter any US adventurism. But unintentionally, a Ukrainian Boeing 373 was shot shown near Tehran minutes after takeoff.
Iranian officials have admitted that human error was responsible for downing the passenger plane and expressed regret and apologized for the tragedy.
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