* US manufacturing unexpectedly contracts in June * Weak factory output raises QE3 expectations * Asian manufacturing data adds to global growth concerns * Investors mull last week's European rescue proposals By Chris Reese NEW YORK, July 2 (Reuters) - U.S. Treasury debt prices rose on Monday as data showing unexpectedly weak U.S. manufacturing last month added to global growth concerns, stoking an appetite for lower-risk investments. Price gains were extended and 30-year bonds traded over a point higher in price after data showed the U.S. manufacturing sector contracted in June for the first time since July 2009. "Not only was the headline poor, but it fell below break even for the first time since the recession. New orders were well below expectations, suggesting a weak hand off in the second half of the year," said Jacob Oubina, senior U.S. economist at RBC Capital Markets in New York. "The implication here is a very soft second half of the year," he said. The U.S. factory data added to speculation the Federal Reserve may do another round of asset purchases, known as QE3, which could perhaps be announced as soon as the central bank's next policy meeting July 31 - Aug. 1. "There is a very good chance of QE3 at the August Fed meeting," Oubina said. Early in the day, Treasuries had firmed following purchasing managers surveys out of China, Japan, South Korea and Taiwan showed demand from importing centers such as Europe and the United States slowed in June. That took the shine off an agreement by European leaders last week to let their rescue fund inject aid directly into stricken banks from next year and intervene in bond markets to support troubled members. Having had the weekend to digest the new measures, some investors are now questioning whether the rescue fund will have enough power to cool down any selling pressure in the large Italian and Spanish debt markets. Worries are also growing over a long implementation process. Benchmark 10-year Treasury notes on Monday were trading 22/32 higher in price to yield 1.57 percent, down from 1.64 percent late Friday. Benchmark yields have been trading in a range of 1.56 percent to 1.73 percent since early June, after yields hit a record low of 1.44 percent on June 1. The Institute for Supply Management said its index of national factory activity fell to 49.7 from 53.5 the month before, missing expectations of 52.0, according to a Reuters poll of economists, and below even the lowest forecast of 50.5. It was the first time since July 2009 that the index has fallen below the 50 mark that indicates contraction. While adding to worries over the pace of global growth, the manufacturing data supported expectations the Fed will move ahead with QE3. The central bank already has purchased $2.3 trillion in mortgage-related and government debt in an effort to depress borrowing costs. In June, the Fed extended its current stimulus program, under which it is selling shorter-dated securities and buying longer-dated Treasuries. Investors are also nervously considering the prospect of the economy hitting a "fiscal cliff" with the scheduled expiration of tax cuts and deep automatic spending cuts early next year. "We look for 10-year yields to rise to 1.7 percent in the third quarter and 1.9 percent by year end," said Ralph Axel, interest rate strategist at Bank of America Merrill Lynch in New York, adding "the main driver would be a partial resolution of the fiscal cliff combined with the beginning of a large scale QE program in September." Thirty-year Treasury bonds on Monday were trading 1-24/32 higher in price to yield 2.67 percent, down from 2.75 percent late Friday.