As the fallout from the Brexit rattles financial markets around the world, one country geographically close to all the drama may be pleased with the United Kingdom's decision to leave the European Union.

Russian Press Secretary Dmitry Peskov has repeatedly signaled since before the vote that his boss, President Vladimir Putin, has no skin in the game. But others disagree.

"It's a clear positive for Russia," Ian Bremmer, president of the geopolitical consultancy Eurasia Group, told CNBC. "Putin wants a weak Europe and a weak trans-Atlantic relationship, and it will help him undermine the U.S.-led sanctions regime as well as maintain a stronger lock on downstream energy relations to the continent."

The United States and European Union have held Russia under economic sanctions in retaliation for Putin's intervention in Ukraine's civil war.

"Publicly, Putin hasn't made a meal of this. Privately, he's surely rather pleased with himself," Bremmer said.

After the results of the referendum were clear, Peskov alluded to the idea that the results could improve Russia's ties to the U.K., which are, like its relations with most Western countries, on the uneasy side.

On Friday, however, Russian Prime Minister Dmitry Medvedev acknowledged that the U.K. decision would create risks for global financial markets.

Ian Brzezinski, senior fellow at the Atlantic Council's Brent Scowcroft Center on International Security, told CNBC that those who support Putin will take the decision as "clear proof that the unity and strength of the West is diluting, if not fragmenting."

"Moscow is likely to conclude that the Russo-phobe camp in the EU has just lost a key pillar," Brzezinski said, "and the Russo-phile camp has consequently gained strength."

Former U.S. Ambassador to Russia Michael McFaul took to Twitter shortly after the votes were in and echoed the sentiment that this was a major win for Putin.

Some, however, say it's not so clear when it comes to whether Russia stands to benefit from the U.K.'s historic vote.

"This makes Russia's rhetoric about the hollowness of Western values and institutions more persuasive, which is good for Moscow, but on the other hand it throws down a gauntlet to the remaining EU leaders who I think will be under pressure to maintain unity on sanctions at the end of the year," Matthew Rojansky, director of the Kennan Institute at the Wilson Center, told CNBC.

Russian stocks have also fallen significantly since the U.K.'s decision.

Moscow's RTS index (Russian Trading System-RTF: .IRTS) was down 3.04 percent on Friday and 2.6 percent Monday.

Edward Mermelstein, a New York attorney who advises wealthy individuals in Russia and the former Soviet Union, just returned from Moscow and said that "the sentiment is that Britain, being a proponent of EU sanctions, will be less of an influence on Europe."

"In other words," Mermelstein said of the Russians, "they were happy to indifferent."

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