"The Syrian leadership firmly intends to create all necessary conditions for the country's development along the path of peaceful transformation, the consolidation of society and the unification of all its healthy forces," said Umakhanov who is leading a delegation of Russian senators to Damascus.
The Syrian people must decide its fate on its own, without any outside interference, Umakhanov said.
"I am sure that the Syrian people will have sufficient wisdom, self-possession and political will," he said.
The Syrian government has used force to crush the opposition protests, and at least 2,200 people have died in violence since March, according to the United Nations estimates.
Moscow favors a political solution to the six-month confrontation between the Syrian authorities and the opposition, while the United States and the European Union have called on Assad to quit.