Iran is keen to enhance its relations with the European Union member states including Latvia, Velayati and Rinkevich In the meeting.
Rinkevich, for his part, welcomed development of bilateral ties with Tehran.
In the meeting, Velayati and Rinkevich also discussed the latest regional and international developments.
Rinkevich is the first senior Latvian official to visit Iran since independence of that country in early 1990s.
Latvia, Estonia and Lithuania are the Baltic group of states. Latvia is also a member of the European Union (EU) and the North Atlantic Treaty Organization (NATO). It joined euro countries in 2014.