(Updates prices; adds details and investor comments) By Noel Randewich and Ross Kerber July 10 (Reuters) - Longer-term U.S. Treasury yields rebounded on Friday, following Wall Street higher as optimism about an antiviral drug to treat COVID-19 countered worries about the economic fallout from a record rise in coronavirus cases in the United States. The yield on the benchmark 10-year U.S. Treasury note rose 2.8 basis points to 0.6332%, after dipping as low as 0.569% earlier in the session - its lowest level since April 22. Gilead Sciences reported that additional data from a late-stage study showed that its antiviral drug remdesivir significantly improved clinical recovery and reduced the risk of death in COVID-19 patients. "The market is trading on the expectation that the economy is not going to shut down for a second time. It is looking past the short term," said Andrew Richman, managing director of fixed income at Truist/SunTrust Advisory Services. Still, more than 60,500 new COVID-19 infections were reported across the United States on Thursday, according to a Reuters tally, setting a one-day record. Robert Kaplan, president of the Federal Reserve Bank of Dallas, in a television interview Friday said that muting the virus' spread is key to an economic recovery, echoing similar recent comments by other Fed policy makers. A closely watched part of the U.S. Treasury yield curve measuring the gap between yields on two- and 10-year Treasury notes, seen as an indicator of economic expectations, was at 48 basis points, almost 2 basis points higher than at Thursday's close. At one point it touched 42.7 basis points, the lowest level since May 4. The two-year U.S. Treasury yield, which typically moves in step with interest rate expectations, was up less than a basis point at 0.1549%, while the five-year yield rose 2.4 basis points to 0.2976%. Even with Friday's reversal, the 10-year yield was down about 5 basis points for the week. "We are heading into the weekend, and investors may be clearing their minds and just booking some profits in fixed-income land," said Kevin Flanagan, head of fixed income strategy at WisdomTree Asset Management in New York. July 10 Friday 11:37AM New York / 1837 GMT Price Current Net Yield % Change (bps) Three-month bills 0.13 0.1322 -0.002 Six-month bills 0.1475 0.1497 -0.005 Two-year note 99-241/256 0.1549 0.004 Three-year note 99-210/256 0.1851 0.010 Five-year note 99-196/256 0.2976 0.024 Seven-year note 100-28/256 0.484 0.030 10-year note 99-236/256 0.6332 0.028 20-year bond 100-92/256 1.1048 0.021 30-year bond 98-40/256 1.325 0.016 DOLLAR SWAP SPREADS Last (bps) Net Change (bps) U.S. 2-year dollar swap 6.00 0.00 spread U.S. 3-year dollar swap 4.00 0.00 spread U.S. 5-year dollar swap 3.25 0.00 spread U.S. 10-year dollar swap -1.75 0.50 spread U.S. 30-year dollar swap -46.75 1.25 spread (Reporting by Ross Kerber in Boston and Noel Randewich in San Francisco Editing by Nick Zieminski and Leslie Adler)