Lavrov met with Janez Lenarcic, director of the Office for Democratic Institutions and Human Rights (ODIHR) on Friday, as part of the Organization for Security and Cooperation in Europe's foreign ministerial meeting in Helsinki.
"The Russian side voiced support for Lenarcic's efforts to correct unilateral approaches to the activities of the ODIHR," the ministry said.
"The need for faster work on drawing up coordinated rules for international electoral monitoring was singled out as a priority. Lenarcic was presented with proposals from Russia and other OSCE member states," the statement said.
Russia's leadership has frequently criticized the work of the ODIHR, which has refused to monitor Russian elections.
The ODIHR boycotted Russia's parliamentary elections last December, citing visa delays and "unprecedented restrictions." The OSCE subsequently declared the elections "not fair."
The organization also refused to monitor Russia's March presidential election, again citing restrictions imposed by Russian election authorities.