* Cypriot parliament rejects bank levy * Bond rally squeezes shorts, prompts short covering * Fed buys $3.14 billion in notes due 2020-2023 By Luciana Lopez NEW YORK, March 19 (Reuters) - U.S. Treasuries prices climbed on Tuesday as a plan in Cyprus to tax bank accounts to help pay for a bailout unraveled, creating uncertainty about the island country's financial future and reviving fears about the stability of the euro zone. Benchmark yields hit a two-week low. The Cypriot parliament overwhelmingly rejected a proposed levy on bank deposits, a proposal that had sent investors dumping stocks and scurrying for safe havens this week. The rejection by Cyprus's parliament of the levy brings the country, one of the euro zone's smaller members, to the brink of financial collapse. Treasuries are being dogged by contagion fears, said Jason Rogan, managing director in Treasuries trading at Guggenheim Partners in New York. "There are some people saying it could occur in Italy and Spain, that is really where the fear is building and why Treasuries are reacting the way they are," he said. Robert Tipp, chief investment strategist for Prudential Fixed Income, said, "It's pretty much wide open on the rumor mill for Cyprus right now. "People are at a loss. There are a lot of factors in play," he said, calling the situation a "jump ball" that could go in many possible directions. Further fueling the rally in Treasuries, investors who had positioned for more gains in yields on strengthening U.S. economic data were caught by surprise and have had to cover short sales. "Cyprus killed any move to higher yields as of right now," Rogan said. Benchmark 10-year notes were last up 13/32 in price to yield 1.910 percent, down from 1.96 percent late on Monday. Thirty-year bonds gained 30/32 in price to yield 3.135 percent, down from 3.18 percent. "The outcome in Cyprus will be the main driver of the markets right now," said Justin Lederer, an interest rate strategist at Cantor Fitzgerald in New York. "There are still many issues out there, and a lot of that's not solved, and that's what keeps the underlying bid in the safe havens," he said. The news from Cyprus overshadowed the Federal Reserve's two-day policy meeting that began on Tuesday. Investors are watching for signs of when Fed Chairman Ben Bernanke might consider tapering or ending bond purchases as recent data have pointed to gathering momentum in the world's biggest economy. Most Wall Street economists expect the Fed will continue its bond purchases through 2013 before tapering or ending the buybacks in 2014. Uncertainty in Cyprus, and fears that it may spread into other countries in the euro zone and harm economic prospects there, might give the Fed further reason to continue its bond purchases, traders said. The Fed bought $3.14 billion in notes due 2020 and 2023 on Tuesday as part of its ongoing purchase program.