(Changes comment, updates prices) By Rodrigo Campos NEW YORK, Sept 14 (Reuters) - U.S. government bond yields fell on Tuesday after data showed consumer prices increased at their slowest pace in six months in August, suggesting that inflation had probably peaked and removing urgency from the next move by the Federal Reserve. The yield on the benchmark 10-year note fell more than 6 basis points on the day to a low of 1.263%, the lowest reading since Aug. 24. The core measure of U.S. consumer prices edged up 0.1% last month, the smallest gain since February. The measure, which excludes the volatile food and energy components, increased 4.0% on a year-on-year basis after advancing 4.3% in July. The data could be volatile in the coming months as shortages of basic materials and parts have created bottlenecks, and price increases, across various supply chains. The August slowdown gives the Federal Reserve breathing room as it prepares to reduce its massive bond holdings and decide how soon to begin lifting rates from near zero. "When the CPI print came out earlier today, and the miss on inflation to the downside, yields started to turn lower and it just seems that the market is interpreting the miss as an indication that the Federal Reserve will simply be more dovish when it comes to monetary policy going forward," said Jim Barnes, director of fixed income at Bryn Mawr Trust. The yield on 10-year Treasury notes was down 4.7 basis points to 1.277%. The 30-year Treasury bond yield was down 5.4 basis points to 1.850%. The two-year U.S. Treasury yield, which typically moves in step with interest rate expectations, was down 0.6 basis points at 0.209%. The U.S. Treasury yield curve measuring the gap between yields on 5- and 30-year Treasury notes was at 106.7 basis points, the flattest since August 2020. The flatter 5/30 spread points to traders losing interest in the reflation story, in line with cooling inflation. The spread between 2- and 10-year Treasury yields , was at 106.6 basis points. The breakeven rate on five-year U.S. Treasury Inflation-Protected Securities (TIPS) was last at 2.512%, after closing at 2.554% on Monday. A pullback in U.S. stock indexes further pressured yields lower mid-morning according to Tom di Galoma, managing director at Seaport Global Holdings. "Equities seem to be struggling a bit and there"s a flight to quality behind it taking place," he said. September 14 Tuesday 3:10PM New York / 1910 GMT Price Current Net Yield % Change (bps) Three-month bills 0.04 0.0406 -0.005 Six-month bills 0.05 0.0507 0.000 Two-year note 99-214/256 0.209 -0.006 Three-year note 99-214/256 0.4301 -0.011 Five-year note 99-218/256 0.7806 -0.024 Seven-year note 100-96/256 1.0689 -0.036 10-year note 99-192/256 1.2769 -0.047 20-year bond 99-128/256 1.7799 -0.054 30-year bond 103-112/256 1.8498 -0.054 DOLLAR SWAP SPREADS Last (bps) Net Change (bps) U.S. 2-year dollar swap 10.00 0.25 spread U.S. 3-year dollar swap 11.50 0.75 spread U.S. 5-year dollar swap 10.00 0.50 spread U.S. 10-year dollar swap 2.50 0.25 spread U.S. 30-year dollar swap -25.00 1.00 spread (Reporting by Rodrigo Campos and Karen Brettell; Editing by Marguerita Choy and Will Dunham)