* Cyprus concerns fade, paring safety bids for bonds * Solid data support view of slow, steady U.S. growth * Sturdy demand seen for $35 bln in two-year note supply * U.S. Fed to buy $2.75 bln-$3.50 bln in government debt By Richard Leong NEW YORK, March 26 (Reuters) - U.S. government debt prices fell on Tuesday as traders trimmed their bond holdings amid reduced anxiety over Cyprus' banking woes ahead of a $35 billion auction of two-year note supply. 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. "It's a combination of different things. The immediate threat from Cyprus has faded. The data have been pretty solid," said John Brady, managing director of interest rate futures sales at R.J. O'Brien & Associates in Chicago. Benchmark 10-year yields retraced 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, which would hurt investors and savers, could cause a possible bank run across the euro zone. 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 0.2630 percent, higher than 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 down 3/32 in price for a yield of 1.928 percent, up 0.8 basis points from late on Monday. The 30-year bond was 4/32 lower in price, yielding 3.151 percent, up half a basis point from Monday's close. The U.S. central bank planned to buy $2.75 billion to $3.50 billion in Treasuries due in May 2020 to Feb. 2023 at 11:00 a.m. (1500 GMT), which is part of its ongoing bond purchases in a bid to hold down long-term interest rates to help the economy.