* US manufacturing unexpectedly contracts in June * 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 on Monday after data showing 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. Earlier 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 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 firepower 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 were trading 19/32 higher in price to yield 1.58 percent, down from 1.64 percent late Friday. 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. In the wake of the ISM data, 30-year Treasury bonds were trading 1-12/32 higher in price to yield 2.69 percent, down from 2.75 percent late Friday.