During the meeting in Tehran on Wednesday, Levichev called for close cooperation between the two sides' banks as well as private sectors to help boost economic exchanges between Iran and Russia.
Expansion of parliamentary cooperation between Iran and Russia would be effective in enhancing their political and cultural relations, he added.
Iran and Russia have vast cooperation in different fields, specially in political and economic spheres.
The two enjoy also special position on the international scene and have long held constant consultations on key regional and global issues.
Russian banks are participating in schemes to finance Iranian oil exports, which are the target of US and European sanctions against Tehran, Russian Energy Minister Alexander Novak said earlier this month.
"Large (banks) are not taking part. Small ones are, yes," Novak told reporters, in the first such confirmation by a top Russian official.
"Major banks are not involved as they have taken into consideration the possibility of any sanctions to which they might become subject".
