* Yields rise to highest levels since August 2011 * Selloff seen complicating $7 bln, 30-yr TIPS auction * Fed to buy $2.75 bln - $3.50 bln notes due 2020-2023 * MOVE volatility index rises to highest in a year By Karen Brettell NEW YORK, June 20 (Reuters) - Benchmark U.S. Treasuries yields rose to their highest in almost two years Thursday after Federal Reserve Chairman Ben Bernanke said Wednesday U.S. growth was strong enough for the Fed to start slowing its stimulative bond purchases later this year. Bernanke downplayed concerns about falling inflation, saying that the Fed expects price pressures to rise back towards its 2 percent target and that the jobless rate should continue to decline to around 7 percent next year, by which point bond purchases are likely to end. The statements were more hawkish than some had expected and promoted broad selling across bonds, with five- and seven-year notes suffering the most. Selling continued overnight, with benchmark 10-year notes yields breaking above technical support to trade at their highest levels since August 2011. "(The Fed has) begun to think about removing accommodation, as opposed to a one-way message that appeared to the market of accommodation as far as the eye can see," said Jim Vogel, an interest rate strategist at FTN Financial in Memphis Tennessee. Yields came off their overnight highs in U.S. trading and fell slightly after data showed that the number of Americans filing new claims for unemployment rose more than expected last week, but not enough to signal a material shift from the recent pace of moderate job growth. Benchmark 10-year notes were last down 12/32 in price to yield 2.41 percent, after earlier rising as high as 2.47 percent overnight, the highest since August 2011. In overnight trading, the yields cracked above support at 2.39 percent, a level last reached in March 2012. Five-year notes fell 6/32 in price to yield 1.30 percent, after earlier increasing to 1.36 percent, the highest since August 2011. Thirty-year bonds dropped 23/32 in price to yield 3.46 percent, after trading as high as 3.53 percent, the highest since September 2011. The Fed will buy between $2.75 billion and $3.50 billion in notes due from 2020 to 2023 on Thursday as part of its ongoing purchase program. Reduced appetite for bonds may complicate the Treasury's auction of $7 billion in a 30-year Treasury Inflation-Protected Securities (TIPS) reopening on Thursday. TIPS, which are typically less liquid than other Treasuries, have borne the brunt of some of the heaviest selling of U.S. government debt as investors are less concerned that Fed policy will add to price pressures. Yields on 10-year TIPS traded at their highest since October 2011 on Thursday, at 28 basis points. Concerns about inflation had pushed the yields into negative territory. That has since reversed for 10-year bonds as inflation readings fall and on higher expectations that the Fed's bond purchase program will be wound down. Data will continue to be scrutinized for signs of further economic momentum, though the recent selloff suggests that more bond investors agree with Bernanke that risks of another slowdown have fallen. "Right now people are pricing a tapering occurring some time before the end of the year, but certainly if all of a sudden you get some bad economic data you could see a rally in the market pretty hard," said Jason Rogan, managing director of Treasuries trading at Guggenheim Partners in New York. Some investors are also worried that markets have become increasingly comfortable with the Fed's stimulative purchases, and that the longer they run, the more volatile an exit from the stimulus measures will be. Volatility measures jumped on Wednesday to their highest levels in around a year. The Merrill Lynch MOVE index , which estimates future volatility of long-term bond yields, increased to 86.9. It is up from a multi-year low of around 50 at the beginning of May.