* U.S. 10-year, 20-year, 30-year yields fall to 3-week lows * U.S. two-year note auction shows decent results * U.S. 2-year/10-year yield curve hits narrowest in 3 weeks * U.S. 10-year swap spreads widen as risk aversion rises * Investors focus on FOMC meeting this week (Adds comment, 10-year swap spreads, updates prices) By Gertrude Chavez-Dreyfuss NEW YORK, Jan 25 (Reuters) - U.S. Treasury prices rose on Monday, pushing long-dated yields to three-week lows, as risk appetite ebbed amid persistent worries about surging virus cases and weak economic growth. Doubts about whether the Biden administration"s proposed $1.9 trillion stimulus plan could push through in Congress also weighed on U.S. yields. Yields on benchmark 10-year, 20-year and 30-year securities all fell to three-week troughs. The yield curve also flattened on Monday, in line with the fall in long bond yields, with the gap between U.S. two-year and 10-year notes dropping to 90.70 basis points, its narrowest spread in three weeks. "The buying...is part technical and fundamentally related to the pandemic in the EU, the looming resignation of Italy"s prime minister, and Senator (Charles) Schumer"s goal to get stimulus passed in the next four to six weeks," said Jim Vogel, senior rates strategist, at FHN Financial in Memphis, Tennessee. Italian Prime Minister Giuseppe Conte will hand in his resignation to the head of state on Tuesday after a morning cabinet meeting to inform his ministers, Conte"s office said. Conte lost his majority in the upper house Senate last week. "A lot can go wrong, or right, in four to six weeks, as traders remember from stimulus deadlines that rolled from July to December," Vogel noted. The U.S. Senate is aiming to pass COVID-19 relief legislation before former President Donald Trump"s impeachment trial begins in early February, a lawmaker said on Monday. As the stimulus relief is being considered, U.S. coronavirus deaths have surged to nearly 420,000 late on Sunday, with 25 million known cases, according to a Reuters tally. In late trading, the U.S. benchmark 10-year yield fell to 1.03%, from 1.091% late on Friday. Monday"s level was the lowest since since Jan. 6. U.S. 30-year yields slid to 1.791% from Friday"s 1.856%, after earlier dropping to a three-week low of 1.789%. The break-even inflation rate on 10-year TIPS, meanwhile, which measures expected annual inflation for the next 10 years, dropped to 2.005%, its lowest since late December. It was last at 2.01%, down from Friday"s 2.017%. Also on Monday, the Treasury"s $60 billion auction of U.S. two-year notes showed decent results. The high yield of 0.125% was below the "when-issued" level or consensus estimate at the bid deadline, wile the bid-to-cover ratio, a gauge of demand, was solid at 2.67 versus an average of 2.52. Investors are also focused on this week"s Federal Open Market Committee meeting, expected to produce little fireworks. In other sectors of the bond market, spreads on 10-year U.S. interest rate swaps over Treasuries widened on Monday, in line with the overall risk-off theme. Spreads of interest rate swaps are typically viewed as indicators of market risk. A higher positive spread suggests overall risk aversion. The spread on 10-year U.S. swaps over benchmark Treasuries rose as high as 3.25 basis points on Monday, the widest gap since mid-October last year. January 25 Monday 4:28PM New York / 2128 GMT Price Current Net Yield % Change (bps) Three-month bills 0.075 0.0761 -0.003 Six-month bills 0.085 0.0862 -0.003 Two-year note 100-2/256 0.1209 -0.004 Three-year note 99-216/256 0.1778 -0.010 Five-year note 99-220/256 0.4038 -0.030 Seven-year note 99-96/256 0.7176 -0.046 10-year note 98-144/256 1.0295 -0.061 20-year bond 96-68/256 1.5957 -0.063 30-year bond 96-36/256 1.7927 -0.063 DOLLAR SWAP SPREADS Last (bps) Net Change (bps) U.S. 2-year dollar swap 7.75 0.25 spread U.S. 3-year dollar swap 8.00 0.25 spread U.S. 5-year dollar swap 9.50 0.25 spread U.S. 10-year dollar swap 3.00 1.00 spread U.S. 30-year dollar swap -24.25 0.50 spread (Reporting by Gertrude Chavez-Dreyfuss; Editing by Will Dunham, Andrea Ricci and Cynthia Osterman)