(Recasts with two-year note auction results, adds analyst comments, updates yields) By Gertrude Chavez-Dreyfuss and Karen Pierog NEW YORK, May 25 (Reuters) - U.S. Treasury yields fell to fresh multi-week lows and the yield curve flattened on Tuesday as an auction of two-year notes attracted solid demand from the market. The benchmark 10-year Treasury yield fell to its lowest level since May 10 at 1.564% following the auction. It was last down 4.1 basis points at 1.5672%. The 30-year yield, which tumbled to its lowest since May 7 at 2.263%, was last 3.6 basis points lower at 2.2654%. The $60 billion of two-year notes were sold at a high yield of 0.152% and a bid-to-cover ratio, a gauge of demand, of an above-average 2.74. "Overall, the stats generated by the auction were very, very strong," Tom Simons, money market economist at Jefferies, wrote in a market report. "It looks like the flood of cash that has been sloshing around the extreme front-end of the curve (bills, repo, etc) has spilled over into the front-end of the coupon curve as well." The two-year Treasury yield, which typically moves in step with interest rate expectations, was last down less than a basis point at 0.1453%. Investor concerns about inflation have eased in response to what the U.S. Federal Reserve has preached over the past few weeks. On Monday, Fed Board Governor Lael Brainard addressed inflation fears, saying she expects that spikes in prices associated with supply bottlenecks and the reopening of the economy to "subside over time." That message was consistent with what Fed Chair Jerome Powell has said repeatedly over recent weeks. "The Fed has been pounding the table every chance it gets that inflation is not a concern at this stage. If we get a few days without such commentary, does the fear re-emerge?," said Ellis Phifer, managing director in fixed income research at Raymond James in Memphis, Tennessee. "It has every time so far but with less effect. The longer end of the Treasury curve, which is most susceptible to inflation, has been trading sideways to slightly lower in yield since topping in March," he added. The yield curve flattened for a fourth straight session, as investors bought the long end of the curve on the view that price pressures would be stable for the rest of the year. A closely watched part of the yield curve that measures the gap between yields on two- and 10-year Treasury notes was last 3.17 basis points flatter at 141.82 basis points. In the repo market, the overnight rate rose to 0.02% from -0.1% on Monday - the lowest since late March. Coronavirus support payments have pumped up the supply of cash in the financial system, along with the Fed"s asset purchases. Part of that cash found its way to the Fed"s reverse repurchase agreement facility, which pays 0%. On Tuesday, the amount awarded by the Fed for its daily operation climbed to nearly $433 billion. May 25 Tuesday 2:01 PM New York / 1801 GMT Price Current Net Yield % Change (bps) Three-month bills 0.015 0.0152 0.000 Six-month bills 0.035 0.0355 0.001 Two-year note 99-246/256 0.1453 -0.008 Three-year note 99-214/256 0.3055 -0.016 Five-year note 99-222/256 0.7775 -0.030 Seven-year note 100-40/256 1.2264 -0.038 10-year note 100-136/256 1.5672 -0.041 20-year bond 101-72/256 2.1705 -0.039 30-year bond 102-96/256 2.2654 -0.036 DOLLAR SWAP SPREADS Last (bps) Net Change (bps) U.S. 2-year dollar swap 8.50 -0.25 spread U.S. 3-year dollar swap 11.00 -0.25 spread U.S. 5-year dollar swap 8.25 0.00 spread U.S. 10-year dollar swap -3.75 -0.50 spread U.S. 30-year dollar swap -29.75 -0.25 spread (Reporting by Gertrude Chavez-Dreyfuss in New York; additional reporting by Karen Pierog in Chicago Editing by Mark Heinrich and Steve Orlofsky) Our Standards: The Thomson Reuters Trust Principles.