* Prices pare losses after jobless claims rise * Prices stay slightly lower before 7-year note sale * Fed will buy $1.25 bln to $1.75 bln bonds due 2036-2043 By Karen Brettell NEW YORK, May 30 (Reuters) - U.S. Treasuries pared price losses on Thursday after data showed the number of Americans filing new claims for unemployment benefits unexpectedly rose last week, but bonds remained down ahead of a new sale of seven-year notes. Investors are increasingly sensitive to economic data since Federal Reserve Chairman Ben Bernanke said last week that the U.S. central bank may decide to taper its program of buying Treasuries and mortgage-backed securities within the next few Fed policy meetings if data shows the economy is gaining steam. Yields have surged this month on improving economic sentiment and as investors sold bonds on concerns about losses should the Fed pull back on its massive bond purchases. Data also showed that a drop in government spending dragged more on the U.S. economy than initially thought in the first three months of the year. "We're very hyper-sensitive to the employment side of things, though the GDP's an old number," said Tom Tucci, head of Treasuries trading at CIBC in New York. The recent backup in rates may help the Treasury sell $29 billion in seven-year notes on Thursday, the final sale of $99 billion in new coupon-bearing debt this week. The government saw strong demand on Wednesday for a $35 billion auction of five-year notes. "Yesterday we had a real bid come back into the market. Now it looks like we're going to gravitate to possibly higher prices but we do have to take this seven-year note out of the way," said Tucci. Benchmark 10-year notes were last down 4/32 in price to yield 2.13 percent, after rising as high as 2.16 percent before the data. The yields have surged from 1.61 percent at the beginning of May, and reached a 13-month high of 2.24 percent in overnight trading on Wednesday. Thirty-year bonds were down 3/32 in price to yield 3.27 percent, after rising to 3.29 percent before the data. These yields rose as high as 3.37 percent on Wednesday, and have increased from 2.81 percent at the beginning of May. The Fed will buy between $1.25 billion and $1.75 billion in debt due 2036 and 2043 on Thursday as part of its bond purchase program.