(Recasts; updates yields, adds analyst comments and upcoming auctions) By Karen Pierog CHICAGO, June 3 (Reuters) - U.S. Treasury yields, particularly in the belly of the curve, climbed on Thursday in light trading ahead of the government"s May employment report. The benchmark 10-year yield was last up 3.4 basis points at 1.625%. Yields on five- and seven-year notes hit two-week highs. The spread between five-year notes and 30-year bonds was last 2.16 basis points flatter at 145.53 basis points. Justin Lederer, Treasury analyst at Cantor Fitzgerald in New York, said yields rose amid low trading volume and improving economic data, but remain range bound. "Data"s a little better, but we just don"t go anywhere," he said. He added that the U.S. Federal Reserve"s statement that it will gradually offload its portfolio of exchange-traded corporate bond funds starting June 7 "was not by any means an announcement of tapering" its government bond purchases. Many analysts expect the Fed to disclose tapering plans at its Jackson Hole economic symposium in August. The market"s immediate focus is on the U.S. Labor Department"s May employment report due out on Friday. According to a Reuters survey of economists, private payrolls likely increased by 600,000 jobs last month after rising by only 218,000 in April. With government hiring expected to have increased by about 50,000, that would lead to overall payrolls advancing by 650,000 jobs in May. The economy created 266,000 jobs in April. Jim Vogel, senior rates strategist at FHN Financial in Memphis, Tennessee, said the market is looking for a broader picture of where the economy was headed. "Tomorrow"s jobs report will be very important, but there"ll still be people waiting to see how the (consumer price index) and retail sales numbers come out," he said. Thursday"s ADP National Employment Report showed private payrolls increased by 978,000 jobs last month, the biggest increase since June 2020. Data for April was revised down to show 654,000 jobs added instead of the initially reported 742,000. Economists polled by Reuters had forecast private payrolls would increase by 650,000 jobs. The number of new claims for unemployment benefits fell below 400,000 last week for the first time since the COVID-19 pandemic began last year, the Labor Department reported on Thursday. Initial claims fell 20,000 to a seasonally adjusted 385,000 for the week ended May 29. The Institute for Supply Management"s (ISM) non-manufacturing activity index rebounded to 64 last month, the highest reading in the series" history, from 62.7 in April. A reading above 50 indicates growth in the services sector, which accounts for more than two-thirds of U.S. economic activity. Economists polled by Reuters had forecast the index climbing to 63.0. The Treasury Department announced auctions next week for $58 billion of three-year notes, $38 billion of 10-year notes, and $24 billion of 30-year bonds. The amount of money flowing into the Fed"s reverse repurchase facility rose to $479 billion on Thursday from $438.7 billion on Wednesday, but remained under a record $485 billion reached on May 27. A flood of cash is pushing down short-term rates and fueling expectations the Fed will take action to maintain its key policy rate. The two-year Treasury yield was 1.3 basis points higher at 0.1604%. A closely watched part of the yield curve that measures the gap between yields on two- and 10-year Treasury notes was last about 2 basis points steeper at 146.11 basis points. June 3 Thursday 3:15PM New York / 1915 GMT Price Current Net Yield % Change (bps) Three-month bills 0.02 0.0203 0.000 Six-month bills 0.0375 0.038 0.003 Two-year note 99-238/256 0.1604 0.013 Three-year note 99-198/256 0.3274 0.024 Five-year note 99-140/256 0.8429 0.047 Seven-year note 99-172/256 1.2993 0.042 10-year note 100 1.625 0.034 20-year bond 100-128/256 2.2188 0.017 30-year bond 101-172/256 2.2974 0.017 DOLLAR SWAP SPREADS Last (bps) Net Change (bps) U.S. 2-year dollar swap 7.75 -0.25 spread U.S. 3-year dollar swap 11.50 -0.25 spread U.S. 5-year dollar swap 7.50 -0.50 spread U.S. 10-year dollar swap -3.00 0.00 spread U.S. 30-year dollar swap -28.75 -0.50 spread (By Karen Pierog; Editing by Andrea Ricci and Jonathan Oatis) Our Standards: The Thomson Reuters Trust Principles.