The Kremlin is maintaining a wall of silence on Ukraine, apart from saying the political crisis must be resolved without foreign pressure.
President Putin has been an open supporter of Mr Yanukovych
However, Russia is clearly watching the events with intense interest.
What happens in Ukraine matters a great deal to Moscow, not least because this could result in another foreign policy blunder for President Vladimir Putin.
The Russian leader visited Ukraine twice during the election campaign, in order to support the pro-Russian candidate, Prime Minister Viktor Yanukovych.
Mr Putin was also the first foreign leader to congratulate Mr Yanukovych when he was initially declared the winner of the now disputed election.
Russia's blatant intervention makes a mockery of President Putin's accusation that the West is meddling in Ukraine and his statement that no-one should interfere in the electoral process.
The Mayor of Moscow, Yuri Luzhkov, fuelled more controversy when he was welcomed at a pro-Yanukovych rally in eastern Ukraine at the weekend.
Mr Luzhkov's attendance was strongly criticised by Yulia Tymoshenko, the firebrand aide of the Ukrainian opposition leader, Viktor Yushchenko.
"Politicians in Russia should simply watch what is happening. Ukrainians can find their own decision, and do what their country needs", said Ms Tymoshenko.
At the heart of President Putin's foreign policy is a desire to formally maintain Russia's sphere of influence in the Commonwealth of Independent States - the countries that made up most of the Soviet Union.
However, writing in The Moscow Times this week, Nikolai Petrov of the Carnegie Moscow Centre argued that Mr Putin's actions had led to a rise of anti-Russian sentiment in Ukraine and around the world.
"The Kremlin's enormous investment in the Ukrainian election not only failed to strengthen but actually weakened Russia's standing on the world stage", said Mr Petrov.
The opposition message is clear: "Putin! Hands off Ukraine"
"This intervention disrupted the Kremlin's ongoing attempt to integrate post-Soviet space, which even before this election, was widely viewed as neo-imperialistic."
Nevertheless, on the domestic front, Mr Putin has moved to place more power in the hands of the Kremlin since the Beslan school siege in the summer, and without much international censure.
The Russian leader is still regarded by the West as an important ally, particularly in the war on terror.
While Ukraine has made no secret of its desire for closer European integration and membership of Nato, President Putin is known to be extremely wary of an enlarged European Union on his doorstep.
In this highly-charged atmosphere, Mr Putin has been accused by his critics of trying to split Ukraine.
Some in the mainly Russian-speaking east of the country are opposed to any move towards Europe, and have been demanding greater autonomy.
Russia, with important EU trade links in mind, won't want to widen the current rift in EU-Russian relations by aggravating Ukraine's instability.
However, it would not be the first time that Moscow had encouraged separatism in the countries of the former Soviet Union, notably in Georgia and Moldova.
So, might Russia intervene militarily in Ukraine?
The respected Russian defence analyst, Pavel Felgenhauer, thinks such a scenario is highly unlikely.
"Putin's Russia does not have the military power to send in the tanks and dominate foreign countries", says Mr Felgenhauer.
"We cannot even bring Chechnya into line. What could we hope to achieve in Ukraine, with its rebellious population of nearly 50 million?"