* U.S. weekly jobless claims unexpectedly fall * U.S. forecast to have added 160,000 new jobs in February * Treasury next week to auction 3-year, 10-year, 30-year bonds By Chris Reese NEW YORK, March 7 (Reuters) - U.S. Treasuries prices fell for a fourth consecutive session on Thursday as a surprise drop in jobless claims added to signs of a strengthening labor market and raised hopes the world's largest economy was gaining steam. The fall in weekly jobless claims came a day after data from payrolls processor ADP showed unexpectedly strong hiring by private employers last month, and boosted expectations for the size of jobs growth in February payrolls data to be released on Friday. "ADP was certainly strong enough that people are whispering for a stronger (payrolls) figure, especially after jobless claims," said Steve Van Order, fixed income strategist at Calvert Investments in Bethesda, Maryland. "People are trying to get themselves prepared for a possible surprise stronger labor market report tomorrow." Benchmark 10-year notes traded 15/32 lower in price to yield 1.991 percent, up from 1.936 percent late Wednesday. Yields reached to as high as 1.997 percent, marking the highest since Feb. 25. The number of Americans filing new claims for unemployment benefits fell to a seasonally adjusted 340,000 last week, below the median from analysts polled by Reuters for a reading of 355,000. "This is not a sign of a slowly growing economy," said Chris Rupkey, chief financial economist at Bank of Tokyo-Mitsubishi UFJ in New York. "This is not an economy that needs to be strengthened by Federal Reserve policy four years after the recession ended." Still, he said, "the bond market remains focused, to the extent it trades at all with the 800 pound gorilla of Fed (quantitative easing) on its back, on the unemployment rate." The government will release its closely watched monthly report on the labor market on Friday. The median of forecasts from analysts polled by Reuters was for the U.S. economy to have added 160,000 new jobs last month, down from 157,000 new jobs in January. The unemployment rate is expected to remain unchanged from January at 7.9 percent. The fall in claims for unemployment benefits in the latest week bolstered stocks on Thursday, pushing the Dow to an intraday record for a third session. The February payrolls report on Friday is key because the Federal Reserve has said it will keep interest rates near zero until the unemployment rate falls to 6.5 percent, as long as inflation does not threaten to top 2.5 percent. The Fed buying of $85 billion of mortgage-backed securities and Treasuries per month has helped fuel global appetite for riskier assets. Planned sales of U.S. government debt next week added to the bearish tone in Treasuries on Thursday as investors pushed for price concessions ahead of the auctions. The Treasury will sell $32 billion of three-year notes on Tuesday, $21 billion of reopened 10-year notes on Wednesday and $13 billion of reopened 30-year bonds on Thursday.