* U.S. 10-year yield hit record low below 1.45 pct * U.S. 30-year yield touches historic low * Weak job data stoke talk of more Fed bond purchases * Record low mortgage rates might not help housing By Richard Leong NEW YORK, June 1 (Reuters) - U.S. government debt yields dropped to record lows on Friday after a stunningly weak report on U.S. job growth stoked worries of an economic slowdown and raised bets for a third round of bond purchases from the Federal Reserve. The soft U.S. employment figures reinforced the view of a global economic slowdown, caused in part by Europe's debt crisis that has raged for more than two years. Contagion fears from a possible Greek exit from the euro and Spain's banking troubles have further driven this week's stampede into cash and low-risk government debt. U.S. Treasuries' rock-bottom yields and Washington's own fiscal problems have not deterred the global chase for investment safe-havens, analysts and investors said. "There is a potential for Treasuries to go up in price in a further flight-to-quality," said Bill Irving, a portfolio manager with Fidelity Investments in Merrimack, New Hampshire, who oversees about $45 billion in bonds. U.S. Treasuries just finished their best month since September. Barclays' Treasury index rose 1.71 percent in May, making it the highest returning U.S. bond sector last month. Benchmark 10-year Treasury notes were up as much as 1-4/32 in price with a yield of 1.442 percent, the lowest level in records going back to the early 1800s, according to data gathered by Reuters. They last traded up 25/32 with a 1.479 percent yield, down nearly 9 basis points on the day. The unrelenting bid for Treasuries could send benchmark yields closer to the 1-percent mark, an unlikely scenario 2-1/2 months ago when some analysts had predicted the end of the 30-year secular bull run for Treasuries. The 10-year note yield peaked near 2.40 percent in mid-March, almost 1 point above its current level. An outcome of these very low Treasuries yields is record low mortgage rates, which are benchmarked against Treasuries. The interest rates on 30-year fixed-rate mortgages averaged a record low of 3.94 percent in the latest week, according to Bankrate.com. Bankrate.com's senior financial analyst Greg McBride said it is possible the average 30-year rate could fall to 3.75 percent if bond yields fall further. McBride, however, said cheap loans in themselves are not enough to stimulate home sales and refinancing if consumers feel uneasy about the labor market. The May jobs report "is a double-edge sword for potential home buyers. We are getting these low mortgage rates, but people are not going to buy a home if they don't feel warm and fuzzy about the jobs market," he said. WORSENING U.S. JOBS PICTURE Friday's poor jobs figures punctuated this week's slew of disappointing U.S. economic data. American employers added 69,000 workers in May, far short of the 150,000 predicted by economists. The jobless rate unexpectedly edged up to 8.2 percent from 8.1 percent in April, the U.S. Labor Department said on Friday. "There's no positive spin that can be put on the May employment report. It was a disappointment, pure and simple," said Jim Baird, chief investment strategist at Plante Moran Financial Advisors in Kalamazoo, Michigan. Adding to investor worries was a private group's report that showed slower U.S. manufacturing growth in May. Fears the euro-zone debt crisis is spilling over to the United States sparked fresh buying of U.S., German, Japan, Swiss and Nordic government debt, which are perceived as safe havens in times of market turbulence. Wall Street stocks extended this week's sell-off with the Standard & Poor's 500 losing 2 percent. Germany, in an effort to offer some relief to its struggling neighbors, softened its push for severe budget cuts across the euro zone on Friday. The move helped lower the borrowing costs for Spain and Italy, although they remained at unsustainable levels. Friday's 10-year note yield surpassed the record low set on Thursday of 1.53 percent. The 10-year yield is on track to fall almost 27 basis points for the week, which would be the biggest weekly drop since early November. The 30-year bond last traded up 1-29/32 in price for a yield of 2.55 percent, down nearly 9 basis points from Thursday's close. The 30-year yield earlier touched 2.510 percent, a record low. The 30-year yield is poised to decline about 29 basis points from a week ago, which would be the biggest weekly fall since late September. In the futures market, Treasury futures, with the exception of two-years, hit contract highs. The September ultra bond contract last traded up 3-15/32 at 172-15/32 after touching a contract high of 174-3/32 earlier. Short-term U.S. interest rates futures for delivery in 2014 and beyond implied traders now see no chance the Federal Reserve will raise until second quarter of 2015. The Fed has pledged it would not budge from its near-zero rate policy target until at least late 2014. In fact, May's dismal jobs data intensified speculation the U.S. central bank will embark on more bond purchases in a bid to avert a recession. Fed policy-makers as recently as this week appeared split on whether more stimulus could lower unemployment. The latest payroll report "might bring a forceful response from policymakers," said Fidelity's Irving, adding, "the Fed policymakers have their fingers on the trigger, but they are not ready pull it yet."