* Fed restarts QE3, buys $1.39 billion in long-dated bonds * U.S. ISM services index unexpectedly falls, factory orders rise * Bond gains curbed by coming government, corporate supply * U.S. Senate seen confirming Yellen as Fed chair By Richard Leong NEW YORK, Jan 6 (Reuters) - U.S. Treasuries prices rose on Monday after weaker-than-expected data on the U.S. services sector raised hopes the Federal Reserve would slow its reduction of bond purchases, spurring bids for government debt. The early 2014 losses on Wall Street after its stellar run last year rekindled some safe-haven appetite for U.S. government debt, analysts and traders said. Medium and long-dated U.S. yields have retreated from their 2-1/2 year highs set last week with the 10-year yield falling below the key 3 percent threshold. But yields could resume their rise on further proof that the domestic labor market is creating jobs at a monthly clip of about 200,000, analysts said. If employers were to hire workers at that pace in December, it would support the view that the Fed will keep dialing back its third round of quantitative easing this year. "We had a run of stronger-than-expected data in December that pushed the 10-year yield above 3 percent. We are now seeing some weaker data so we are seeing it falling below 3 percent," said Stan Shipley, bond strategist at ISI Group in New York. On Dec. 18, Fed policymakers said the central bank would buy $75 billion in Treasuries and mortgage-backed securities per month starting in January - a reduction of $10 billion in its monthly purchases - on evidence of an improving economy. Last Friday, Fed Chairman Ben Bernanke gave an upbeat outlook on the economy at an event in Philadelphia, but he cautioned that the recovery "clearly remains incomplete." Monday's data supported Bernanke's view of the uneven recovery. The Institute for Supply Management said its index on services fell in December, while the Commerce Department said new orders for factory goods rebounded in November following a drop in October. "The number that matters is Friday's payrolls number," Shipley said. Economists polled by Reuters estimated U.S. employers added 195,000 jobs last month, compared with 203,000 in November, while they forecast that the jobless rate held at a five-year low of 7.0 percent. The benchmark 10-year U.S. Treasury note rose 8/32 in price to yield 2.963 percent, down 3 basis points from late on Friday. The 30-year bond, after climbing nearly 1 point in price, ended up 19/32 to yield 3.894 percent, down 3.5 basis points from Friday. The 10-year note's yield hit a near 2-1/2-year high of 3.041 percent last Thursday, while the 30-year bond's yield touched 4.001 percent a week ago, which was its highest intraday level since early August 2011, according to Reuters data. The U.S. central bank restarted its QE3 program on Monday after a hiatus during the Christmas and New Year holidays. It bought $1.391 billion of Treasuries due from May 2036 to August 2043. In other Fed developments, the U.S. Senate is expected to confirm Janet Yellen to succeed Bernanke as chair of the central bank in a vote scheduled late Monday afternoon. If confirmed, Yellen will be the first woman to serve as the Fed's top official. For Wall Street, Yellen's tenure as Fed chief would likely support the notion that the Fed will stick with an aggressive stimulus, which has kept interest rates low and stoked the recovery in the housing and stock markets that were hammered during the Great Recession. The Fed's resumption of its bond buys came as the Treasury Department prepared to sell $30 billion in three-year debt on Tuesday, $21 billion in 10-year notes on Wednesday and $13 billion in 30-year bonds on Thursday. In "when-issued" activity, traders expected the upcoming three-year issue to sell at a yield of 0.8070 percent, which would be the highest yield at a three-year auction since September. Traders anticipated solid demand for the three-year notes given the relatively wide yield gap between two-year and three-year Treasuries, but they were less certain about the bidding for longer maturities before Friday's payroll data. "People are comfortable with the three-year part of the curve because they think it's the sweet spot with the rolldown and some people think the Fed won't raise rates until 2016," said Thomas Roth, executive director of U.S. government bond trading at Mitsubishi UFJ Securities USA in New York. Competing for investors' cash will be an expected heavy wave of investment-grade corporate bonds, which analysts say should rebound following a poor 2013. Bond dealers forecast that companies plan to sell $90 billion to $100 billion in high-grade debt in January, according to IFR, a unit of Thomson Reuters.