(Updates prices, analyst comment, reverse repo data) By Chuck Mikolajczak NEW YORK, July 6 (Reuters) - U.S. Treasury yields fell on Tuesday, with the benchmark 10-year note poised for its longest streak of daily declines in 16 months as investors look for clues on the Federal Reserve"s policy path and after data signaled the service sector expanded at a slower pace. A gauge of activity from the Institute for Supply Management on the U.S. services sector, which accounts for about two-thirds of economic activity, showed moderate growth in June, down from the record pace in May. The data comes on the heels of Friday"s employment report, which was viewed by many as showing an improving labor market, but not enough to signal an economy that may be prone to overheating. "Seems to have been at least some reaction to the ISM services print showing the Employment sub-index in contractionary territory for the first time since Dec. 2020," said Zachary Griffiths, rates strategist at Wells Fargo. "While employment in contractionary territory could be considered concerning, comments from the release suggest the weakness is driven more by a lack of labor supply, not a lack of demand." Analysts also pointed to volatility in the oil market, where crude had run up in price until faltering on Tuesday after OPEC producers canceled a meeting, China"s crackdown on Chinese tech stocks listed in the United States such as Didi Global and position reshuffling after a long holiday weekend as contributing to the drop in yields. The yield on 10-year Treasury notes was down 6.4 basis points to 1.368%. The yield hit a low of 1.352%, its lowest since Feb. 24 and was on track for a sixth straight session of declines. Investors will turn their focus to Wednesday"s release of minutes from the Fed"s June 15-16 meeting, when officials opened debate on how to end crisis-era bond-buying and signaled interest rate increases were closer on the horizon than previously thought. The amount of cash flowing into the Fed"s overnight reverse repurchase operation edged up to $772.5 billion from the $731.5 billion on Friday, but short of Wednesday"s record high $992 billion. The yield on the 30-year Treasury bond was down 4.9 basis points to 2.001%, having earlier fallen below the 2% mark for the first time since June 21. The breakeven rate on five-year U.S. Treasury Inflation-Protected Securities (TIPS) was last at 2.491%, after closing at 2.502% on Friday, near its highest close in a month. A closely watched part of the U.S. Treasury yield curve measuring the gap between yields on two- and 10-year Treasury notes, seen as an indicator of economic expectations, was at 114.5 basis points from 119 on Friday. July 6 Tuesday 3:10PM New York / 1910 GMT Price US T BONDS SEP1 162-5/32 1-8/32 10YR TNotes SEP1 133-60/256 0-144/25 6 Price Current Net Yield % Change (bps) Three-month bills 0.0475 0.0482 -0.003 Six-month bills 0.05 0.0507 -0.002 Two-year note 99-207/256 0.2219 -0.016 Three-year note 99-136/256 0.4106 -0.032 Five-year note 100-80/256 0.8109 -0.051 Seven-year note 100-204/256 1.1309 -0.065 10-year note 102-92/256 1.3682 -0.064 30-year bond 108-96/256 2.001 -0.049 DOLLAR SWAP SPREADS Last (bps) Net Change (bps) U.S. 2-year dollar swap 7.75 -23.50 spread U.S. 3-year dollar swap 11.50 -44.25 spread U.S. 5-year dollar swap 7.25 -0.25 spread U.S. 10-year dollar swap -2.75 -0.25 spread U.S. 30-year dollar swap -31.75 -0.50 spread (Reporting by Chuck Mikolajczak; Additional reporting by Karen Pierog and Kate Duguid; Editing by Andrea Ricci) Our Standards: The Thomson Reuters Trust Principles.