"According to the officially announced results of Iran's presidential election, it was won by current President Mahmoud Ahmadinejad," Russia's Foreign Ministry said in a statement.
"We consider all issues linked to Iran's election as this country's exclusively internal affair. We believe the discords that emerged after the election must be settled in strict conformity with the Islamic Republic's constitution and laws."
Iran's opposition leader Mirhossein Mousavi, who was officially beaten into second place by Ahmadinejad in an election Mousavi says was rigged, called late on Sunday for fresh protests by his supporters.
Iran's hardline Revolutionary Guards threatened on Monday to crush protests.
U.S. President Barack Obama, at the forefront of diplomatic efforts to halt an Iranian nuclear program the West fears could yield atomic weapons, has urged Iran to stop violence against protesters.
Iranian authorities have accused Western powers of supporting the widespread street protest after the election and have not ruled out expulsions of some European ambassadors.