Andrey Slepnev made the remarks in a meeting with the Iranian Ambassador to Russia Kazem Jalali, IRNA reported.
He also called the agreement the most important cooperation document between the two sides.
Jalali, for his part, said the FTA is the result of intensive negotiations and the will of the two sides to develop bilateral relations.
In 2018, Iran and the EAEU inked a preferential trade agreement (PTA), which came into effect on October 27, 2019. The two sides later began negotiations to upgrade the PTA to FTA, after the success of the former.
The EAEU was established in 2015 at the initiative taken by the Russian Federation, Kazakhstan, and Belarus. Afterward, Armenia and Kyrgyzstan joined the union.