* Yields rise on concerns that Fed will taper in September * Investors sell bonds, mortgage hedging adds to weakness * Fed buys $1.59 billion bonds due 2036-2043 By Karen Brettell and Luciana Lopez NEW YORK, Aug 19 (Reuters) - Longer-dated U.S. Treasuries yields rose to two-year highs on Monday, extending weakness after their worst week in two months, as investors worried about the effect on the market if the Federal Reserve reduces its bond purchase program next month. Benchmark 10-year note yields have risen by more than a full percentage point from 1.60 percent at the beginning of May, when Fed Chairman Ben Bernanke said the U.S. central bank may pare back its bond purchases, surprising many investors. Improving economic data has added to expectations that the Fed will begin reducing purchases next month, sending 10-year yields to near 2.90 percent on Monday. Investors who had bet on falling yields have also had to sell those positions, adding to weakness. "A lot of portfolios have been liquidating. As we get closer to the tapering, clearly people want to be out of the way of that," said Scott Graham, head of U.S. government bond trading at BMO Capital Markets in Chicago. More stringent capital rules for banks are also likely reducing demand for government bonds. Lighter volumes as traders take summer vacations, and hedging by mortgage servicing companies, are also adding to the yield increase, Graham said. Seven-year notes yields rose as high as 2.29 percent on Monday, the highest since July 2011. They have increased from around 2 percent a week ago and are up from 1.05 percent at the beginning of May. Benchmark 10-year Treasury notes yields rose as high as 2.90 percent, also the highest since July 2011. They are up from around 2.60 percent a week ago and from 1.60 percent at the beginning of May. Thirty-year bonds yields jumped to 3.91 percent, the highest since August 2011. They have risen from 3.60 percent a week ago and from around 2.80 percent at the beginning of May. With little economic data, the next focus for investors is the release on Wednesday of the Fed's meeting minutes from July, which will be evaluated for any signs of the pace and timing of a pullback from the $85 billion a month stimulus. The minutes will be "one of the few opportunities to get any type of insight into where the policy is leaning ahead of the potential taper announcement," said Ian Lyngen, senior government bond strategist at CRT Capital Group LLC in Stamford, Connecticut. A Reuters poll showed Wednesday that a majority of economists expect the Fed to reduce bond purchases at its Sept. 17-18 policy meeting, with a consensus expecting the U.S. central bank would reduce purchases by $15 billion initially. The Fed bought $1.59 billion in bonds due between 2036 and 2043 on Monday as part of its ongoing purchase program. It will buy between $0.75 billion and $1.00 billion in debt due from 2024 and 2031 on Tuesday. The release of the minutes will be followed by the annual policy conference held each year by the Fed in Jackson Hole, Wyoming, which will be on Thursday and Friday. Fed Chairman Ben Bernanke will not be attending, unlike in previous years. His absence comes as investors await news on who will be the next chairman of the U.S. central bank. Fed Vice Chairman Janet Yellen and former Treasury Secretary Lawrence Summers are considered the front-runners. The market is likely to remain data-dependent heading into the influential jobs report for August, which will be released on September 6, with housing data also likely to be scrutinized for any signs that the back-up in rates is weighing on the housing recovery. "If there is softening in the housing data, which is one of the pillars of strength, then you have to recognize that as a pretty significant shift. But if we can get through this period without higher rates having a dampening effect, then we will probably continue the move towards higher rates as the Fed begins to taper," said BMO's Graham.