(Corrects headline, first paragraph to remove reference to hitting new 13-month peak in two-year yields) By David Randall NEW YORK, June 21 (Reuters) - Two-year Treasury yields edged closer to their highest levels since March 2020 while longer-dated bond yields inched higher Monday as investors continued to digest the Federal Reserve"s hawkish turn at its policy meeting last week. The Fed said Wednesday that most policymakers expect two interest rate hikes in 2023. The prospect of those sooner-than-expected moves have pushed short-term yields higher while keeping longer-duration yields in check as market fears of out-of-control inflation subside. "By bringing forward rate hikes, the Fed is providing a material headwind not only for any inflation that might not prove transitory but also growth as well. Needless to say, such a hawkish pivot is likely to remain topical for weeks to come – a reality further reinforced by the lack of meaningful economic data over the next several sessions," said Ian Lyngen, head of U.S. rates strategy at BMO Capital Markets. Two-year yields rose to 0.2684%, while 10-year yields edged higher to 1.4667%. Bond yields rise as prices fall. "It feels like the Fed’s modest moves last week basically got them in line with where the street was already. The bond markets seem to agree with that, as the yield on the U.S. 10-year ended the week below 1.5%," said Arthur Hogan, chief market strategist at National Securities. Investors will be watching for comments from St. Louis Fed President James Bullard and New York Fed President John Williams later in the day. Price Current Net Yield % Change (bps) Three-month bills 0.04 0.0406 0.000 Six-month bills 0.055 0.0558 0.003 Two-year note 99-185/256 0.2684 0.010 Three-year note 99-66/256 0.5012 0.021 Five-year note 99-56/256 0.9121 0.026 Seven-year note 100-8/256 1.2452 0.026 10-year note 101-100/256 1.4734 0.023 20-year bond 103-228/256 2.0117 0.035 30-year bond 106-188/256 2.0717 0.044 DOLLAR SWAP SPREADS Last (bps) Net Change (bps) GooU.S. 2-year dollar swap 6.75 0.25 spread U.S. 3-year dollar swap 7.25 -0.50 spread U.S. 5-year dollar swap 4.50 -0.50 spread U.S. 10-year dollar swap -3.75 0.50 spread U.S. 30-year dollar swap -31.75 -0.75 spread (Reported by David Randall; editing by Jonathan Oatis) Our Standards: The Thomson Reuters Trust Principles.