* Longer-dated yields recede from four-month highs * Fed buys longer-dated Treasuries, sells shorter-dated * New York Fed business index lowest since April 2009 By Chris Reese NEW YORK, Sept 17 (Reuters) - U.S. Treasury debt prices rose o n M onday as investors did some bargain-hunting following a sharp sell-off last week that was tied to inflation fears and reduced safety bids on optimism about the European debt crisis. Longer-dated yields retreated from their highest levels since May, which were set o n F riday when investors sold Treasuries on fears a Federal Reserve plan to do a third round of bond purchases would fuel rising inflation. Monday's "bounce in Treasuries was a function of attractive levels rather than fundamentals," said Ian Lyngen, senior government bond strategist at CRT Capital Group in Stamford, Connecticut. Weaker U.S. economic data and concerns about slowing growth in China also revived some bids for bonds, pushing yields lower. "Rates will grind lower in the short term because economic data will remain tepid," said Eric Green, global head of rates and FX research and strategy with TD Securities in New York. The New York Federal Reserve said on Monday its measure of regional business activities unexpectedly worsened in September, falling to its lowest level since April 2009. Investors have been assessing the longer-term impact of the open-ended bond-buying programs from the Fed and the European Central Bank with the goals of lowering unemployment and averting a regional recession, respectively. They are concerned that by injecting more cash into the banking system, the two central banks are hurting their currencies and will have a tougher time containing inflation once economic growth normalizes. The Fed said last Thursday it will buy $40 billion a month in mortgage-backed bonds on an open-ended basis, its third round of bond buying, or quantitative easing, dubbed QE3. It also prolonged its pledge to hold interest rates near zero into mid-2015, from late 2014. "The reflation trade is not going away," said Charles Comiskey, head of Treasury trading at Bank of Nova Scotia. He added that the Fed is squarely focused on reducing unemployment while tolerating higher inflation. This perception has fueled a rally in Treasury Inflation-Protected Securities since the Fed began QE3 on Friday. The yield premiums, or inflation breakeven rates, on regular Treasuries over TIPS jumped broadly. The 10-year TIPS breakeven rate, which gauges investors' inflation expectations, touched 2.64 percentage points on Friday, the highest since April 2011, according to Reuters data. On Monday the 10-year breakeven rate was 2.58 points. Another indicator that showed growing inflation concerns among investors was a steepening yield curve, or widening spreads between shorter- and longer-dated yields. The spread between five-year and 30-year yields ended at 2.37 percentage points on Friday, the widest since September last year. It was at 2.32 points at midday on Monday. The 30-year bond traded 1-6/32 higher in price to yield 3.03 percent, down from 3.09 percent late Friday. The Fed did two operations on Monday under its stimulus program, which has been nicknamed "Operation Twist." It bought $4.74 billion in Treasuries due November 2020 through August 2022, and later sold $7.799 billion in debt maturing December 2014 through May 2015. Operation Twist, which began last year and will continue into the end of this year, was intended to lower mortgage rates and other long-term borrowing costs. Under the program, the Fed sells its holdings of shorter-dated Treasuries and buys longer-dated issues on the open market. Benchmark 10-year notes traded 11/32 higher in price to yield 1.83 percent, down from 1.87 percent late Friday. Trading volume was lighter-than-usual due to a holiday in Japan and the Jewish New Year.