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 dipped but held within their recent ranges in light trading. Two-year note yields, which are highly sensitive to interest rate shifts, have risen to the highest since March 2020, with the Federal Reserve seen 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 two-year yields were last at 0.742%, after earlier reaching 0.758%. Longer-dated yields dipped slightly but held within their recent ranges before the Treasury is due to sell new intermediate-dated debt. The Treasury will sell $57 billion in five-year notes on Tuesday and $56 billion in seven-year notes on Wednesday, when it will also issue $24 billion in two-year floating-rate notes. Five-year note yields were last at 1.239%, down from 1.250% late Monday. Seven-year notes were at 1.395%, down from 1.410%. Benchmark 10-year note yields fell to 1.462%, from 1.477%. The yield curve between two-year and 10-year notes flattened to 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 opened at all-time highs on Tuesday with investors unshaken by Omicron-driven travel disruptions and store closures. Demand for the Treasuries this week is likely muted by illiquid trading conditions with many traders and investors out between the Christmas and New Year"s holidays.