(Updates with market activity, analyst comments) By Ross Kerber June 10 (Reuters) - Traders sent longer-term U.S. Treasury yields higher Thursday after new data showed a further increase of consumer prices in May, steepening a closely watched part of the yield curve. The benchmark 10-year yield was up 2.7 basis points at 1.5161% in morning trading and had reached as high as 1.535%. Much of the movement came after the U.S. Labor Department said its consumer price index increased 0.6% last month after surging 0.8% in April, which was the largest gain since June 2009. Separately, the department said initial claims for state unemployment benefits fell to their lowest level in 15 months. The increase in the 10-year yield broke a pattern of declines in recent days but left the note still below its range of last week. Several analysts said the inflation report was not a major surprise, keeping the focus on what new guidance if any might come from U.S. Federal Reserve officials next week. "I think the market is really buying into the narrative that the rise in inflation is in fact transient because you"re not seeing that necessarily being priced into fears in the bond market," said Subadra Rajappa, head of U.S. rates strategy for Societe Generale. The trading pushed up the 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. It was at 136 basis points, about 2 basis points higher than Wednesday"s close. The 10-year TIPS yield was at -0.843% and the breakeven inflation rate was at 2.354%, still near its lowest since April. The two-year U.S. Treasury yield, which typically moves in step with interest rate expectations, was up less than a basis point at 0.1568%. The yield on the one-month note was at 0.0025%, the lowest since May when it touched 0% for the first time since March 2020. Traders will watch the results of an auction of $24 billion of 30-year Treasury bonds due around 1 p.m. ET. June 10 Thursday 9:24AM New York / 1324 GMT Price Current Net Yield % Change (bps) Three-month bills 0.025 0.0253 0.000 Six-month bills 0.04 0.0406 0.000 Two-year note 99-240/256 0.1568 0.002 Three-year note 99-198/256 0.326 0.013 Five-year note 99-228/256 0.7725 0.027 Seven-year note 100-96/256 1.1938 0.028 10-year note 101 1.5161 0.027 20-year bond 102-16/256 2.1225 0.026 30-year bond 103-220/256 2.1983 0.030 DOLLAR SWAP SPREADS Last (bps) Net Change (bps) U.S. 2-year dollar swap 6.50 0.00 spread U.S. 3-year dollar swap 8.50 0.25 spread U.S. 5-year dollar swap 7.00 0.00 spread U.S. 10-year dollar swap -2.75 0.25 spread U.S. 30-year dollar swap -30.00 -0.25 spread (Reporting by Ross Kerber in Boston Editing by Chizu Nomiyama) Our Standards: The Thomson Reuters Trust Principles.