(Updates yields, adds comments from analyst and Fed official; reverse repo operation) By Karen Pierog CHICAGO, June 28 (Reuters) - U.S. Treasury yields fell on Monday as the market prepared for the release of June employment data later in the week to gauge the strength of the economic recovery from the coronavirus pandemic. The benchmark 10-year yield was last down 5.4 basis points at 1.4816%. Last week, it notched its largest weekly gain since March, but has remained below 1.6% since early June. The market was rallying a bit, perhaps on relatively low volumes and liquidity and without being propelled by any news as it heads into the long July 4th holiday weekend, according to Subadra Rajappa, head of U.S. rates strategy at Societe Generale. "I think a lot of it has to deal with perhaps month-end buying and some position squaring ahead of payrolls on Friday," she added. The U.S. Labor Department is expected to report on Friday that nonfarm payrolls increased by 690,000 in June, after rising by 559,000 in May, according to a Reuters poll of economists. The unemployment rate is forecast to have fallen to 5.7%, from 5.8% in May. George Goncalves, head of U.S. macro strategy at MUFG in New York, said investors will be looking to see just how strong employment was this month. "If we"re to get the numbers we were supposed to get that didn"t happen during Q2, but we"re going to get them in Q3 and Q4, then we"ll see rates continue to climb higher because that gives the window for the (Federal Reserve) to taper," he said, referring to a reduction in the U.S. central bank"s $120 billion in monthly bond purchases. Federal Reserve Bank of Richmond President Thomas Barkin said on Monday that the Fed has made "substantial further progress" toward its inflation goal in order to begin tapering. He also said he was "pretty optimistic" about the labor market. Meanwhile, the amount of cash flowing into the Fed"s overnight reverse repurchase operation remained elevated on Monday at $803 billion. Volume hit a record high of nearly $813.6 billion last Wednesday. The two-year Treasury yield was 1.4 basis points lower at 0.2563%. Yield curves flattened, with the gap between 5- and 30-year yields last shrinking by 2.32 basis points at 120.15 basis points. A closely watched part of the yield curve that measures the gap between yields on two- and 10-year Treasury notes was last about 3 basis points flatter at 122.36 basis points. June 28 Monday 3:11PM New York / 1911 GMT Price Current Net Yield % Change (bps) Three-month bills 0.05 0.0507 -0.002 Six-month bills 0.055 0.0558 0.000 Two-year note 99-189/256 0.2563 -0.014 Three-year note 99-98/256 0.46 -0.021 Five-year note 99-226/256 0.899 -0.030 Seven-year note 100-4/256 1.2477 -0.044 10-year note 101-80/256 1.4816 -0.054 20-year bond 103-128/256 2.035 -0.062 30-year bond 106-16/256 2.1007 -0.068 DOLLAR SWAP SPREADS Last (bps) Net Change (bps) U.S. 2-year dollar swap 7.75 1.25 spread U.S. 3-year dollar swap 10.50 0.50 spread U.S. 5-year dollar swap 6.75 1.00 spread U.S. 10-year dollar swap -3.50 0.75 spread U.S. 30-year dollar swap -32.00 1.00 spread (Reporting by Karen Pierog Editing by Paul Simao and Marguerita Choy) Our Standards: The Thomson Reuters Trust Principles.