The flight comes as last-ditch diplomatic talks between Russia's foreign minister and the US secretary of state to resolve the tensions in Ukraine ended without an agreement.
Markets were nervous before Sunday's Crimea referendum on secession from Ukraine. Traders and businesspeople fear this could spark western sanctions against Russia as early as Monday.
Yields on Russia's 10-year government bonds rose close to 9.7 per cent on Friday, compared with less than 8 per cent in January. The rouble hit 36.7 to the dollar, near to its weakest rate on record.
It also emerged on Friday that Russia's top 10 billionaires, led by Alisher Usmanov, had lost a combined $6.6bn of their net worth over the past week, according to research firm Wealth-X. Russian equities, which showed more weakness on Friday, have lost 20 per cent of their value since the start of the year.
"You don't need to have sanctions in place to cause economic turmoil," said Christopher Granville, managing director of Trusted Sources, an emerging markets research firm. "The expectation is enough."
Strobe Talbott, president of the Brookings Institution, who served in the State Department under Bill Clinton, said: "The irony is that the Russian banking sector has made quite a lot of progress in plugging into the global system. That means it is vulnerable, and a good lever for applying pressure."
Data published by the Federal Reserve Bank of New York sparked speculation that the Russian central bank was also reducing its vulnerability to potential sanctions. The data showed a drop of $105bn in Treasuries held by foreign institutions for the week ending March 12.
"We can only speculate about who might have decided to move their securities out of the Fed and into a third-party custodian, but one obvious candidate is Russia," said Lou Crandall at Wrightson Icap.
Russia held $138.6bn in US government debt at the end of December, according to the US Treasury.
One senior Moscow banker said 90 per cent of investors were already behaving as if sanctions were in place, adding that this was "prudent exposure management".
Traders and bankers said US banks had been particularly heavy sellers of Russian bonds. According to data from the Bank for International Settlements, US banks and asset managers between them have about $75bn of exposure to Russia.
Joseph Dayan, head of markets at BCS, one of Russia's largest brokers said: "It's been quite an ugly picture in Russian bonds the last few days and some of it has to do with international banks reducing exposure."
Although foreign banks have not yet begun cutting credit to Russian companies en masse, bankers said half a dozen live deals to fund some of Russia's biggest companies were in limbo as lenders waited to see how punitive western sanctions would be.
Bankers said Barclays of the UK had withdrawn from a plan with Russia's VTB jointly to fund an Essar Energy deal. Barclays declined to comment.
Alexei Kudrin, a former Russian finance minister and a member of Vladimir Putin's economic council, warned on Thursday that sanctions could drive an extra $50bn of capital outflows from the Russian economy per quarter.
The New York Fed and Russia's central bank declined to comment, as did Sberbank, VTB and Lukoil.
Meanwhile, in a sign of the EU's continuing economic ties to Russia, South Steam, the gas pipeline project backed by Gazprom of Russia, Eni of Italy, EDF of France and BASF of Germany, announced that it had signed a contract worth about €2bn with Saipem of Italy to build the offshore stretch of the route under the Back Sea from Russia to Bulgaria. Construction is scheduled to start in June.