* Cyprus concerns persist, stoke safety bids for bonds * Mixed data support view of steady but slow U.S. growth * Sturdy demand seen for $35 bln in two-year note supply * U.S. Fed buys $3.14 bln medium-term government debt By Richard Leong NEW YORK, March 26 (Reuters) - U.S. government debt prices rose in light, choppy trading on Tuesday as worries about Cyprus's banking problems persisted, supporting safe-haven bids for bonds ahead of the U.S. Treasury's auction of $35 billion in new two-year notes. The Cyprus rescue plan, which averted a collapse of its banking sector, has spurred speculation about whether the plan that involves losses to banks' bondholders and large depositors will become a roadmap for future euro zone bank bailouts. This raised worries about bank runs in Italy and Spain, whose banking systems are many times larger than that of Cyprus. Concerns about Europe, together with mixed U.S. economic data, offset earlier selling inspired by stronger Wall Street stock prices, analysts said. "It's a lot of push-pull today. The market doesn't know what to do," Sharon Stark, chief fixed income strategist at D.A. Davidson & Co. in Tampa said of the day's listless trading. The latest data on domestic home prices and durable goods orders supported a notion that the U.S. economic recovery remained on track, but steeper-than-expected drops in consumer confidence and new home sales undercut hopes that the pace of growth was accelerating. Benchmark 10-year yields rose from their two-week lows set last week on diminished fears over Cyprus' banking system since the island nation obtained a 10 billion euro ($13 billion) international bailout this past weekend. Ten-year yields, however, have stayed below 2 percent on some safe-haven demand for bonds in the wake of comments from Jeroen Dijsselbloem, the head of the Eurogroup of finance ministers, who said on Monday that a Cypriot bailout - which wiped out some senior bank bondholders and will impose big losses on large depositors - will serve as a model for resolving euro zone banking problems. He later appeared to backtrack, saying Cyprus was a specific case with exceptional challenges including vast deposits from Russian overseas investors, but analysts said this "bail-in" solution could cause a possible bank run across the euro zone. Concerns about the impact on the U.S. economy from the euro zone's debt crisis was compounded by the latest data that showed a deterioration in consumer confidence and new home sales, analysts said. "The economy is healing but it's a slow process," said Larry Dyer, chief U.S. interest rate strategist at HSBC Securities USA in New York. "We seem to be stuck in a very narrow trading range." Dyer expected the 10-year yield to bounce between 1.85 percent and 2.05 percent in the near term. The latest flare-up in the festering euro zone debt crisis, together with the Federal Reserve's commitment to hold down interest rates, should feed bids at the two-year auction at 1:00 p.m. (1700 GMT), part of this week's $99 billion in regular coupon-bearing supply, analysts said. In the when-issued market, traders expected the upcoming two-year note supply to yield 0.2580 percent, close to the 0.257 percent yield on the two-year issue sold at the February refunding. On the open market, the 10-year Treasury note last traded up 3/32 in price for a yield of 1.928 percent, down 1.2 basis points from late on Monday. The 30-year bond was 7/32 higher in price, yielding 3.135 percent, down 1.2 basis points from Monday's close. The U.S. central bank bought $3.142 billion in Treasuries due in May 2020 to Feb. 2023, which was part of its ongoing bond purchases in a bid to hold down long-term interest rates to help the economy.