* Most prices pare earlier losses, yields fall from highs * Investors remain nervous over renewed selling * Treasury to sell $35 bln 2-yr notes on Tuesday By Karen Brettell NEW YORK, June 24 U.S. government bond prices bounced back on Monday, with yields falling from near two-year highs, though investors remained nervous that the Federal Reserve could soon pare back its bond purchase program. Fed Chairman Ben Bernanke spooked investors last week when he said the U.S. central bank may reduce its bond purchases in response to an improving economy and falling unemployment rate. Some view volatility since Bernanke's comments as evidence that the market has become hooked on Fed purchases of $85 billion a month in Treasuries and mortgage-backed debt. "The exit door is not that big and everyone's going at the same time," said Justin Lederer, strategist at Cantor Fitzgerald in New York. "This is not just about a Treasury backup, this is a global, everyone-getting-out-of-everything." The market rout has extended from Treasuries to stocks, credit instruments, and emerging markets and volatility across assets also picked up. Long-dated bonds turned positive on Monday afternoon as stocks also came off session lows, giving hope that markets may be close to some stabilization. "Sometimes the selling dries up," said Lou Brien, market strategist at DRW Trading in Chicago, adding that it's still too soon to say that the recent selloff is over. Comments from Federal Reserve Bank of Dallas President Richard Fisher saying the central bank will be running an accommodative policy even if it reduces stimulus may have helped add a bid to bonds. New sales of $99 billion in coupon-bearing supply this week risks adding some further softness to the bond market. The Treasury will sell $35 billion in two-year notes on Tuesday, $35 billion in five-year notes on Wednesday and $29 billion in seven-year notes on Thursday. U.S. 10 year-notes were last up 1/32 in price on Monday to yield 2.54 percent. During the session the yield rose as high as 2.67 percent, the highest since August 2011. The 30-year Treasury bond rose 17/32 to yield 3.56 percent. The yield went as high as 3.65 percent, the highest since September 2011. Treasury Inflation-Protected Securities, or TIPS, were also hard-hit earlier on Monday. Yields on five-year TIPS turned flat on Monday and briefly traded above zero for the first time since February 2011, according to data by TradeWeb. TIPS yields have spiraled in recent sessions, hit by the expectations of the Fed pullback and a subdued inflation outlook. Personal Consumption Expenditures (PCE) data on Thursday for May will be closely scrutinized for signs of whether inflation is stabilizing at lower levels, or rising, or if price pressures are continuing to fall. The index fell to a record low of 1.05 percent over the year in April and a continued fall may make it less likely that the Fed is able to pare back its record stimulus. "The market should not forget that is a key component for them and a persistent low level of inflation is something that will alter the future path of QE," said Brien. The Fed bought $3.68 billion in note due 2019 and 2020 on Monday as part of its ongoing purchases. It will purchase between $1.25 billion and $1.75 billion in bonds due 2036 and 2043 on Tuesday as part of the program.