* Cyprus negotiating deal with Russia * British budget in focus, after BoE minutes * Fed meeting statement and Bernanke news conference awaited By Gertrude Chavez-Dreyfuss NEW YORK, March 20 (Reuters) - The euro rallied on Wednesday from a four-month low hit against the dollar in the previous session, as worries about Cyprus eased with some investors convinced the debt-plagued country will be able to hammer out a deal to avert a default. Europe's common currency, however, remained vulnerable given the underlying uncertainty in the region and the potential risk that what happened in Cyprus could hit other fiscally frail euro zone countries like Spain and Italy. 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 condition for the bailout. But so far, there is no deal on Russia yet. "Headline risks abound with regard to Cyprus, but investors are focused on how it can raise the 5.8 bln 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. So without that tax on bank deposits, Cyprus seems to have other options." The euro was last up 0.5 percent at $1.2955, 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. "Markets in Europe are used to getting a solution at the very last minute," said Lutz Karpowitz, currency analyst at Commerzbank. 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 given that economic data has improved 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 press conference following the FOMC statement. But Kathy Lien, managing director at BK Asset Management in New York said that the FOMC statement, Fed forecasts and Bernanke's comments could send mixed messages as it 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. BRITISH BUDGET In London, British finance minister George Osborne, in his annual budget presentation, said on Wednesday Britain will borrow more in the coming years than official forecasts showed in December and will miss one of its two debt targets by another year. As a result, sterling turned lower in early New York trading at $1.5152, down 0.4 percent on the day. 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 0.5 percent at 95.59 yen, while the euro rose 1 percent to 123.85 yen.