* Prices fall as investors ponder extent of recent rally * Fed statement in focus, QE timeline under scrutiny * Libor rates rise, suggest some fear over euro zone contagion By Karen Brettell NEW YORK, March 20 (Reuters) - U.S. Treasuries yields rose on Wednesday as investors reconsidered whether concern over contagion from Cyprus's debt problems justified much lower yields, and before the Federal Reserve was due to give its statement from its two-day meeting. Benchmark 10-year Treasuries yields have fallen to 1.94 percent by early trade on Wednesday from around 2.06 percent last week, boosted by safe haven buying as Cyprus tries to avert a financial meltdown, which some fear could spread to renewed stress on banks in countries including Italy and Spain. At the same time, improving U.S. economic data is leading some investors to prepare for a gradual march higher in yields and the possible tapering or end to the Federal Reserve's bond purchase program late this year, or early next year. "This morning you're seeing a little bit of a recognition that this market has gone a little too far on a short-term basis, though that doesn't mean it will be a straight line back the other way," said Greg Faranello, a Treasuries trader at Societe Generale in New York. Cyprus pleaded for a new loan from Russia on Wednesday, after the island's parliament rejected the terms of a bailout from the European Union, raising the risk of default and a bank crash. Ten-year Treasuries have largely held in a range between 1.90 percent and 1.95 percent for the last three days. They were down 11/32 in price on Wednesday. Thirty-year bonds fell 20/32 in price to yield 3.16 percent, up from 3.13 percent late on Tuesday. Several banks have raised their submissions in the London interbank offered rate (Libor) this week, spurring some concerns that banks and investors may again be pulling back on loans made in the euro zone region. Despite this move, traders said that there were not yet any signs that Cyprus's problems threaten broader contagion. "There are some accounts that are taking a wait and see approach, but there has been no systemic issue," said Kenneth Silliman, head of short-term rates trading at TD Securities in New York. The three month U.S. dollar Libor rate increased to 28.41 basis points on Wednesday, the highest since March 1, and up from 28.01 basis points on Monday. Some of this increase may be market driven and due to the selloff in Eurodollar futures on Monday and Tuesday, rather than based on fundamental factors, Silliman said. The two-year interest rate swap spread, which is sometimes seen as a proxy for bank credit risk, also retraced from seven month wides on Wednesday. The swap rate tightened to 16 basis points, after widening 19.50 basis points on Tuesday, the widest level since August. Investors are expecting few surprises from the Fed on Wednesday, with Chairman Ben Bernanke seen likely to reference the improving economy while saying that stimulus is likely to continue in order to support further improvement. "I don't suspect we're going to get anything new," said Faranello. That said, "the Fed is buying $85 billion a month, the potential is for that to skew lower not higher." Most Wall Street economists expect that the Fed will taper or end bond purchases at the end of the year.