The opposition said the vote was rigged and international monitors have also questioned the polls.
The ministry said Russia would like peace and order to be restored in the East African country, "based on respect for the Constitution and norms of democracy, so that Kenya could once again serve as an example of stability for the entire region."
The ministry previously said that, "Moscow is following the developments in Kenya and hopes political forces in the country will show restraint and readiness to resolve problems in accordance with the Constitution."
President Mwai Kibaki, 76, recently said he wanted to form a broad government which would include members of the opposition, but he has failed to meet with opposition chief Raila Odinga or suggest how the crisis could be ended.
Former UN Secretary General Kofi Annan is taking over the mediation role in Kenya from the African Union chairman, Ghana's President John Kufuor.
Kufour held talks Thursday with Kibaki and Odinga, but failed to negotiate any breakthrough. Both sides said they would work together with leading African figures under Kofi Annan.
