More than 1,000 people have been killed and around 300,000 forced from their homes in Kenya since violence broke out after the disputed December 27 presidential election, in which Mwai Kibaki gained re-election.
On Tuesday, former United Nations secretary general Kofi Annan chaired peace talks between the government and the opposition.
"Russia welcomes the parties' decision to seek ways of resolving their differences at the negotiating table", the ministry said in a statement.
"We again urge all political leaders in Kenya to prevent the disruption of dialogue, and to respect the commitments they have undertaken to bring the country back to normal life, so that peace and order can be re-established as soon as possible."
The conflict broke out after the opposition, led by Raila Odinga, refused to recognize Mwai Kibaki as the winner of the election, which both international and local observers said was rigged. The fighting escalated into an ethnic conflict, with public anger focusing on the ruling Kikuyu tribe.
In February, the rival factions drafted a plan of joint action to solve the crisis.
As possible resolutions, Kofi Annan, who wants a special commission set up to investigate the violence, suggests a power-sharing deal between the parties, the creation of an interim government before a new presidential vote, and verification of the election results.