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Right Sector is a grouping of far-right and nationalist factions whose activists were among the most radical and confrontational of the three-monthlong demonstrations in the Ukrainian capital, Kiev, which eventually ousted Yanukovych.
The Kremlin statement also claimed Russian citizens trying to enter Ukraine have been turned back at the border by Ukrainian officials.
Pro-Russia sentiment is high in Ukraine's east and there are fears Russia could seek to incorporate that area as well.
Obama has warned that the March 16 referendum in Crimea would violate international law, and Putin countered that in phone calls with German Chancellor Angela Merkel and British Minister David Cameron.
"The steps taken by the legitimate leadership of Crimea are based on the norms of international law and aim to ensure the legal interests of the population of the peninsula," Putin said, according to the Kremlin.
Meanwhile, Obama spoke by telephone with Chinese President Xi Jinping late Sunday, trying to court China's support for efforts to isolate Russia over its military intervention in Ukraine.
Obama appealed to Beijing's vehement opposition to outside intervention in other nations' domestic affairs, according to a White House statement.
Obama "noted his overriding objective of restoring Ukraine's sovereignty and territorial integrity and ensuring the Ukrainian people are able to determine their own future without foreign interference," the statement said, adding that the two leaders "agreed on the importance of upholding principles of sovereignty and territorial integrity."
China has been studiously neutral since the Ukraine crisis began and it remained unclear whether China would side with the U.S. and Europe or with Moscow.
The U.N. Security Council, meanwhile, met on Ukraine for the fifth time in 10 days to hear a closed-door briefing from Ukraine's U.N. Ambassador Yuriy Sergeyev. The council has been unable to take any action because Russia has veto power.
In Kiev, Mikhail Khodorkovsky, the businessman and Putin critic who was once Russia's most famous prisoner, said Monday his country is ruining its longstanding friendship with Ukraine.
"The question of Crimea's fate is very painful both for Ukrainians and for Russians. It's not just a simple territorial dispute for some extra square kilometers," Khodorkovsky told a packed hall at Kiev Polytechnic University.
"For Russians, it's a sacred place, an important element in our historical memory and the most painful wound since the Soviet collapse," Khodorkovsky said. Nevertheless, he said, the symbolism of Crimea for Russians cannot justify "such a blatant incursion into the affairs of a historically friendly state."
He called for Crimea to remain part of Ukraine, but with broader regional powers and the protection of the rights of Russian speakers there.
Khodorkovsky, once Russia's wealthiest man, was pardoned last December by Putin. Many believe he was convicted of tax violations and other crimes and sent to prison on trumped-up charges.
On Sunday, Khodorkovsky almost wept as he urged a large crowd in Kiev's center not to believe that all Russians support their government's actions in Crimea.