* U.S. payrolls grow 175,000 in May, above median forecast * Some see Fed buying fewer bonds starting in September * Ten-year yield set for sixth straight weekly rise * Repo rate on 10-year notes stuck in negative territory By Richard Leong NEW YORK, June 7 (Reuters) - U.S. Treasury debt prices slid on Friday in volatile trading as data that showed mildly better than expected employment growth in May revived bets the Federal Reserve might pare its bond purchases later this year and spurred selling in bonds. The yield on the benchmark 10-year note was on track to rise for a sixth straight week, which has not happened since late March to early May 2009 when the U.S. economy was losing hundreds of thousands of jobs a month during the depths of the Great Recession. The latest U.S. payrolls gain of 175,000, while below the top end of economists' forecasts of above 200,000, was high enough to feed speculation that Fed policymakers will scale back their $85 billion monthly purchases of Treasuries and mortgage-backed securities later this year. The May jobs report was seen as critical evidence for the U.S. central bank's June 18-19 policy meeting where policymakers will likely further discuss the approach to reduce its asset purchases, which have helped propel Wall Street stock prices to record highs and supported the housing recovery. "This is a good report. This puts the Fed tapering theme back in the market," said Eric Green, global head of rates and currency research and strategy at TD Securities in New York. Some traders reckoned the Fed might signal a reduction in bond purchases in the third quarter. "Our expectation would be that you still could have the Fed - starting in and around September - very moderately reduce the scale of their long-term asset purchase program, which generally has been the expectation of the markets," Rick Rieder, co-head of Americas fixed-income at BlackRock, the world's largest asset manager, in New York said during a conference call with reporters after the jobs data. But some economists think that the sluggish pace of U.S. economic growth, which came it at 2.4 percent in the first quarter, and relatively high unemployment, which edged up to 7.6 percent in May, still require the current level of Fed accommodation. In the meantime, the selling in Treasuries was compounded by investors closing Treasuries hedges on their mortgage-backed securities holdings. Any reduction in the U.S. central bank's third round of quantitative easing, dubbed QE3, will likely increase mortgage rates and slow refinancing, reducing the appeal of mortgage bonds, analysts said. Trading volume in the cash and futures markets jumped after the payrolls data. Bond prices gyrated wildly for a short period until they settled into a lower trading range. As of 12 p.m. (1600 GMT), $339.2 billion in Treasuries had changed hands, 23 percent above the 20-day average at this time, according to ICAP, the biggest inter-dealer broker for U.S. government debt. A rally in Wall Street stocks stemming from the May jobs data also reduced the allure of low-yielding government bonds. Disappointing jobs readings from ADP and the Institute for Supply Management this week caused some traders to curb expectations for the May payroll reading, rekindling bids for Treasuries in the two previous trading sessions. Despite the market selloff on Friday, the 10-year Treasury yield held below the 13-month-plus highs set last week and still far less than the 4 percent level prior to the Fed's adoption of its first round of QE back in late 2008. U.S. benchmark 10-year Treasury notes last traded 21/32 lower in price with a yield of 2.154 percent, up 7.7 basis points from late on Thursday. The 30-year bond was down 1-14/32 in price, yielding 3.319 percent, up 7.9. basis points from Thursday's close. In MBS trading, the yield on 30-year, 3.0-percent coupon mortgage bonds guaranteed by Fannie Mae was up nearly 5 basis points at 2.89 percent. Its yield spread to comparable five-year Treasuries widened to 1.85 percentage points from 1.79 points late on Thursday, according to Reuters data. As bond prices renewed their recent slump, exchange-traded funds that bet against Treasuries enjoyed another week of gains. For example, the Proshares Ultrashort 20-plus Treasury ETF was on track to rise 0.47 percent on the week, bringing its year-to-date gain to 7.86 percent. REPO "SPECIAL" PERSISTS In money markets, the supply of 10-year note issues remained scarce or "special" in the repurchase agreement (repo) sector, keeping the overnight borrowing costs to lend them in negative territory. This meant investors pay Wall Street dealers and other holders of the 10-year notes to own them instead of the other way around during normal conditions when there is adequate supply of this maturity. Ten-year repos for over-the-weekend traded at minus 2.75 percentage points early Friday, compared with minus 3.10 percent late on Thursday. The repo "specialness" of 10-year notes has been driven by heavy demand from money market funds and cash investors after a drop in supply of Treasury bills in April. Analysts said the scarcity of 10-year Treasuries will gradually ease after the government sells $21 billion of 10-year supply next week.