* U.S. Dec. private job growth strongest in 13 months-ADP * U.S. 10-year note supply on track for highest yield since 2011 * Fed to buy $1 billion to $1.5 billion in long-dated debt * Fed to release minutes of Dec. 17-18 meeting at 2 p.m. By Richard Leong NEW YORK, Jan 8 (Reuters) - U.S. Treasuries prices fell on Wednesday as an upbeat report on the private labor market signaled faster U.S. economic growth, supporting the view the Federal Reserve would stay on course to wind down its bond purchases in 2014. The encouraging jobs news spurred selling in government bonds in advance of a $21 billion auction of 10-year Treasuries at 1 p.m. (1800 GMT). The market's losses were limited with benchmark yields holding below 3 percent by the Fed's planned purchase of long-dated Treasuries under the third round of its quantitative easing (QE3) program. Traders were also reluctant to sell heavily in case of surprises in the Fed's minutes on its December policy meeting where policy-makers decided to pare QE3 purchases by $10 billion to $75 billion a month, analysts said. The U.S. central bank will release the record its two-day meeting last month at 2 p.m. (1900 GMT). "We are still holding below 3 percent. People are waiting for the minutes. If they speak anymore about the qualitative measures on tapering, they could move bonds later," said Gennadiy Goldberg, interest rate strategist with TD Securities in New York. On the open market, benchmark 10-year Treasury notes were down 12/32 in price, yielding 2.982 percent which was up 4 basis points from late on Tuesday. The 10-year yield touched a two-week low of 2.937 percent on Tuesday after hitting a near 2-1/2-year high of 3.041 percent last week, according to Reuters data. Treasuries yields have risen since last spring after the Fed signaled it will dial back its massive bond purchase stimulus in response to an improving economy. Fed officials, while unemployment has remained higher than where they like, have acknowledged private and public hiring has picked up with consumer demand and business activities. Payroll processor ADP said on Wednesday U.S. companies added 238,000 jobs in December, the strongest monthly rise in 13 months. It also bested the median forecast of 200,000 among analysts polled by Reuters. ADP also upgraded its November figure on private hiring to 229,000 from the initially reported 215,000. Some analysts see the ADP as a predictor for the government's payroll reading. The Labor Department will release its December jobs report at 8:30 a.m. (1330 GMT) on Friday. Economists polled by Reuters forecast U.S. employers likely added 196,000 jobs in December after a 203,000 rise in November. Meanwhile, the Fed will buy $1.00 billion to $1.50 billion in long-dated bonds due in 2036 to 2043 as a part of its planned $40 billion purchases in Treasuries this month. On Monday, it bought $1.39 billion of these maturities. In the wake of the latest ADP report, some investors sought higher yield at the upcoming 10-year auction, part of this week's $64 billion in coupon-bearing government debt. During "when-issued" activity early Wednesday, traders expected the latest 10-year supply to sell at a yield of 2.989 percent, which would be the high yield set at a 10-year auction since May 2011. "It's helping the market to build in a concession for the 10-year auction," TD's Goldberg said of the December ADP data. "It makes today's 10-year auction more challenging," he added. The 10-year supply followed a somewhat disappointing three-year note auction on Tuesday. The Treasury will complete this week's debt offering on Thursday with a $13 billion sale of 30-year bonds. Competing for investors' cash this week has been a heavy wave of investment-grade corporate bonds. Bond dealers projected companies will raise $20 billion to $25 billion in the high-grade market this week, according to IFR, a unit of Thomson Reuters.