* U.S. December private job growth strongest in 13 months - ADP * Fed's Dec. meeting minutes show support for gradual end to stimulus * U.S. sells 10-year notes at highest yield since 2011 * Fed buys $1.31 billion in long-dated Treasuries 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 Fed's release of its Dec. 17-18 policy meeting showed many members on its policy-setting Federal Open Market Committee supported a "measured" pace to end its third round of quantitative easing that began in late 2012, as they saw a declining benefit in continuing the program. The ADP jobs news and worries about details of the Fed's tapering decision spurred selling in government bonds and restrained aggressive bidding at a $21 billion sale of 10-year Treasuries, which fetched the highest yield at a 10-year auction since May 2011. "The argument for higher rates is getting stronger," said Paul Montaquila, fixed income investment officer with Bank of the West and BNP Paribas Securities Corp. in San Francisco. "They are using every opportunity to validate why they are tapering. They want to put the plan in place," he said. The minutes of the Fed's December policy meeting where policy-makers decided to pare QE3 purchases by $10 billion to $75 billion a month were particularly unsettling for short-dated and intermediate Treasuries. The minutes forced some traders to reconsider how quickly the Fed might raise short-term interest rates if the U.S. central bank were to dial back its bond purchases at each policy meeting this year if the unemployment falls further and inflation rises toward its 2 percent target, analysts said. According to CME FedWatch, short-term U.S. interest rates futures implied traders now assign a 60 percent probability for the first Fed rate hike as early as April 2015. This expected short lag between the end of QE3 and the first rate increase spurred the heaviest selling in Treasuries due in three to seven years. The five-year yield rose 9 basis points on the day to 1.762 percent, within striking distance of a four-month high. Benchmark 10-year Treasury notes were down 15/32 in price, yielding 2.993 percent which was up more than 5 basis points from late on Tuesday. The 10-year yield had climbed to 3.010 after the FOMC minutes before some late bargain-hunting emerged and on perception the Fed's tapering path will reduce longer-term inflation risk. Just last week, the 10-year yield hit a near 2-1/2-year high of 3.041 percent, according to Reuters data. Treasuries yields have risen more than 1.25 percentage points since last spring after the Fed signaled it will dial back its QE3 in response to an improving economy. Payroll processor ADP said earlier 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 U.S. Labor Department will release its December jobs report at 8:30 a.m. (1330 GMT) on Friday. Economists polled by Reuters forecast employers likely added 196,000 jobs, down from 203,000 in November. Meanwhile, the Fed will buy $1.31 billion bonds due in May 2038 to May 2043 as a part of its planned $40 billion purchases in Treasuries this month. On Monday, it bought $1.39 billion of these maturities. Between the release of the latest ADP jobs data and the FOMC minutes, some investors positioned for higher yield at the 10-year auction, part of this week's $64 billion in coupon-bearing government debt. 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. A heavy wave of investment-grade corporate bond issues has been competing for investors' cash this week. 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.