* Euro rebounds from four-month low against dollar * Cyprus seeking financial deal with Russia * Fed statement at 2 p.m. (1800 GMT), Bernanke half-hour later By Gertrude Chavez-Dreyfuss NEW YORK, March 20 (Reuters) - The euro rebounded on Wednesday from a four-month low against the dollar in the previous session as worries about Cyprus eased, with some investors convinced the debt-plagued country can hammer out a deal to avert default. Europe's common currency, however, remained vulnerable to uncertainty about Cyprus' bailout and the potential risk that bank deposits in other euro zone countries, like Spain and Italy, could be taxed as a pre-condition for future financial aid. That should fan broader concerns about the euro zone as a whole. Cyprus has sought Russia's help to come up with 5.8 billion euros after its parliament rejected on Tuesday a proposed levy on bank deposits, which would have raised that amount. That levy on deposits was a European Union condition for Cyprus' bailout. But so far, there is no deal with Russia yet. "Headline risks abound with regard to Cyprus, but investors are focused on how it can raise the 5.8 billion euros without the deposit tax," said Brian Dangerfield, currency strategist at RBS Securities in Stamford, Connecticut. "Investors are waiting to see whether Cyprus will be able to get some bilateral deal with Russia, or anything related to its natural has reserves, or selling assets." The euro was last up 0.6 percent at $1.2952, recovering from Tuesday's four-month low of $1.2843 and holding above a key chart support level at the 200-day moving average around $1.2873. One trader said Tuesday's slide was prompting a short-covering rally which could take the euro towards $1.2960. Any rise though could be seen as an opportunity to sell the currency. Some strategists also said the European Central Bank's assurance on Tuesday that it was committed to providing liquidity to Cypriot banks within certain limits had helped curb euro losses. Marc Chandler, global head of currency strategy, at Brown Brothers Harriman in New York, further added that contrary to fears over the weekend, there has not been a run of depositors from banks in the euro zone. "The sovereign bond markets in the periphery had sold off earlier in the week, but have stabilized. This is true even for Greece, which before today had seen its 10-year bond sell off for seven consecutive sessions, with yields rising about 125 basis points," Chandler said. Meanwhile, a Federal Reserve policy decision later on Wednesday could put the euro back under pressure by highlighting the discrepancy between an improving U.S. economy and the fragile euro zone. Asset purchases and interest rates are expected to remain unchanged. That will leave the market's focus on the statement from the Federal Open Market Committee, the forecasts and Fed Chairman Ben Bernanke's comments in light of improved economic data since the last meeting. There has been recent speculation that the Fed could begin winding down asset purchases and Bernanke could be asked about their exit strategy at a news conference following the FOMC statement. But Kathy Lien, managing director at BK Asset Management in New York, said the FOMC statement, Fed forecasts and Bernanke's comments could send mixed messages, which has happened before. "The FOMC statement could recognize recent improvements in economic data and contain a more optimistic tone, but economic projections and Bernanke's comments could be more cautious," Lien said. In Japan, the market was wary of any comments from Haruhiko Kuroda, who becomes governor of the Bank of Japan on Wednesday. Expectations are high that the BoJ will embark on a much more aggressive monetary policy to fight deflation. The dollar was up 0.4 percent at 95.50 yen, while the euro rose 0.9 percent to 123.70 yen.