NEW YORK, Dec 28 (Reuters) - Two-year Treasury yields hit almost two-year highs on Tuesday, following tepid demand for an auction of the notes on Monday, while longer-dated yields ended little changed on the day after demand for new five-year notes was also soft. Two-year note yields, which are highly sensitive to interest rate shifts, have risen to the highest level since March 2020 as expectations increase that the Federal Reserve is closer to raising rates as the U.S. economy rebounds from COVID-19-related shutdowns and inflation surges. A $56 billion auction of two-year notes on Monday saw soft demand, pricing at a high yield of 0.769%, around half a basis point above where they had traded before the sale. The Treasury also drew unenthusiastic demand for a $57 billion sale of five-year notes on Tuesday, which sold at a high yield of 1.263%, also around a half a basis point above where the yields traded before the auction. The auction “was a disappointment thanks to poor pricing and lackluster demand. But those are not surprising given thinning year-end liquidity,” Kim Rupert, managing director of global fixed income analysis at Action Economics, said in a note. Demand for Treasuries this week is muted with many traders and investors out between the Christmas and New Year"s holidays. The Treasury will also sell $56 billion in seven-year notes and $24 billion in two-year floating-rate notes on Wednesday. Two-year yields were last at 0.748%, after earlier reaching 0.758%. Five-year note yields were last at 1.243%, down from 1.250% late on Monday. Seven-year notes were at 1.405%, down from 1.410%. Benchmark 10-year note yields edged higher to 1.479%, from 1.477%. The yield curve between two-year and 10-year notes flattened as far as 71 basis points, the smallest yield gap since Nov. 23. Risk sentiment has improved this week as the Omicron coronavirus variant appears to be less virulent, despite its rapid spread globally. Stocks edged lower after earlier reaching a record intraday high.