By Gertrude Chavez-Dreyfuss NEW YORK, Jan 21 (Reuters) - U.S. Treasury prices surged on Tuesday, pushing yields lower as risk appetite dropped, amid worries about the potential fallout from a lethal virus that has broken out in China. U.S. two-year note yields fell to two-week lows, while those on 10-year and 30-year yields slid after rising in the previous two sessions. Wall Street shares struggled, as well, as investors tried to make sense of this new virus outbreak. Global officials confirmed that the coronavirus strain is contagious between humans. The death toll from a mysterious flu-like virus in China climbed to six on Tuesday as new cases surged beyond 300. "The fear is that it could be a SARS-type event, which was an economic issue," said Ellis Phifer, market strategist at Raymond James in Tennessee. "But this is all cautionary. The market is not panicking or anything." China's Severe Acute Respiratory Syndrome (SARS) outbreak from 2002 to 2003 killed nearly 800 people at the time. In morning trading, U.S. 10-year yields fell to 1.776%, from 1.835% late on Friday. U.S. financial markets were closed on Monday for the Martin Luther King, Jr holiday. Yields on U.S. 30-year bonds were at 2.235%, down from 2.296% on Friday. On the short end of the curve, U.S. two-year yields fell to two-week lows of 1.535% from Friday's 1.569%. They were last at 1.532%. The yield curve flattened on Tuesday after steepening last week, as global rates fell on caution about the coronavirus. The spread between the two-year and 10-year note yields narrowed to 24.47 basis points. Meanwhile, U.S. President Donald Trump's impeachment trial in the Senate, which begins on Tuesday, has also caused some mild jitters. Democrats have called on the Senate to remove the Republican president from office, describing him as a danger to American democracy and national security. Trump and his lawyers have decried his impeachment, saying he has done nothing wrong and that Democrats are simply trying to stop him from being re-elected. "The impeachment trial is finally here," said Raymond James' Phifer. "I don't think the concern is anything more than that. Now that it's here, let's be a little cautious again." January 21 Tuesday 10:15AM New York/1515 GMT Price Current Net Yield % Change (bps) Three-month bills 1.5325 1.5637 0.003 Six-month bills 1.525 1.5621 -0.003 Two-year note 100-44/256 1.5345 -0.035 Three-year note 99-226/256 1.5403 -0.041 Five-year note 100-202/256 1.5832 -0.048 Seven-year note 100-96/256 1.6924 -0.053 10-year note 99-188/256 1.7795 -0.056 30-year bond 102-240/256 2.2393 -0.057 DOLLAR SWAP SPREADS Last (bps) Net Change (bps) U.S. 2-year dollar swap 7.75 0.00 spread U.S. 3-year dollar swap 4.50 0.25 spread U.S. 5-year dollar swap 1.75 0.50 spread U.S. 10-year dollar swap -4.25 0.25 spread U.S. 30-year dollar swap -31.00 0.75 spread (Reporting by Gertrude Chavez-Dreyfuss Editing by Nick Zieminski)