NEW YORK, Dec 31 (Reuters) - U.S. Treasury yields fell on Thursday, the last trading day of the year, pulling the yield curve flatter despite an unexpected drop in unemployment claims in the United States for a second straight week. The decline ran counter to recent trends higher in long-dated yields and a steepening in the Treasury curve on hopes that the distribution of vaccines would help end the coronavirus pandemic, which has plunged the global economy into crisis and killed nearly 2 million people. Emerging hyper-contagious variants of the coronavirus have helped mute vaccine optimism for the moment, and may have contributed to the dip in yields on Thursday, said analysts at Action Economics. “The focus remains on the immediate concerns over the surging virus cases and the new strains which have resulted in renewed and more stringent mitigation measures that are adding to concerns over a slowing in growth momentum.” Though longer-dated yields have risen since the all-time lows hit in March, the 10-year yield closed the year down 100 basis points and the 30-year yield ended the year down 74 basis points. Rates have fallen dramatically as demand for the safe-haven securities has increased during this year’s pandemic-related volatility. Yields have also dropped as the Federal Reserve has ramped up its purchases of Treasury debt in order to bolster the market, although the bulk of its purchases have been at the shorter end of the curve. The Fed’s short-dated Treasury purchases, and interest rate cuts that lowered the central bank’s key overnight lending rate to near zero, pushed the two-year yield down 144 basis points this year. The anchored two-year yield has allowed the yield curve - as measured by the spread between the two- and 10-year yields - to steepen by 44.8 basis points in 2020. The two-year yield is likely to remain near its current level of 0.123% until the U.S. central bank adjusts its interest rate policy. Yields at the long end of the curve could continue to rise - the general trend they have followed since a low in August - if economic data improves in the new year. Initial claims for state unemployment benefits slid to a seasonally adjusted 787,000 for the week ended Dec. 26, from 806,000 in the prior week, the Labor Department said on Thursday. “The weekly claims numbers left some hope for a positive nonfarm payrolls print in just over a week’s time,” said Bill O’Donnell, rates strategist at Citigroup. The U.S. Labor Department will release its closely watched monthly jobs report on Jan. 8. The benchmark 10-year yield on Thursday fell 1 basis point to 0.917%, pulling the spread between the two- and 10-year yields down to 79.2 basis points, the lowest in a week. The yield on the 30-year bond was last down 1.6 basis points at 1.646%. Though the drop in jobless claims is a positive sign for the U.S. economy, thin trading volume skewed the Treasury market’s response to the data. With few people in the office, the Treasury market closing early on Thursday and some international markets already closed ahead of Friday’s New Year’s holiday, yields were being directed by one-off trades rather than broader trends. “Overnight Treasury volume was about 35% of average with some key markets shut,” O’Donnell said. The breakeven rate on the 10-year TIPS, which measures the expected annual inflation for the next 10 years, rose to 1.991% intraday and closed at 1.986%, its highest since November 2018. (Reporting by Kate Duguid Editing by Leslie Adler and Paul Simao)