* U.S. auction of $29 bln 7-year notes last of week * Fed to skip U.S. government debt purchases on Thursday By Richard Leong NEW YORK, April 25 (Reuters) - U.S. Treasuries prices slipped on Thursday as investors prepared for an upcoming $29 billion auction of seven-year notes, the last part of the government's $99 billion offerings of longer-dated debt this week. Although the market was modestly weak due to the new supply, bond yields remained locked in a tight trading range, as investors awaited fresh clues on the state of the labor market and the Federal Reserve's assessment on the economy next week. Fed policy-makers will meet next Tuesday and Wednesday, and the closely watched monthly payrolls report for April will be released at the end of the week, on May 3. Trading between buyers and sellers has been evenly matched with benchmark yields almost unchanged so far this week, analysts said. "When things are this balanced, whenever there's any little blip, there's a counter-position that emerges," said Jim Vogel, interest rate strategist at FTN Financial in Memphis, Tennessee. Bond prices briefly fell earlier after the government reported that new claims for jobless benefits fell more than expected, offsetting a recent wave of disappointing albeit bond-friendly data. Claims for new jobless benefits fell to 339,000 last week, the U.S. Labor Department said. Benchmark 10-year Treasury notes were down as much as 7/32 in price in reaction to the jobless claims. They last traded 5/32 lower at 102-16/32, with a yield of 1.720 percent, up 1.7 basis points from Wednesday. The 10-year yield was about 7 basis points above a more than four-month low of 1.643 percent set on Tuesday. In "when-issued" activity, traders expected the new seven-year note issue due in April 2020 to sell at a yield of 1.1620 percent, which is lower than the 1.248 percent in March and on track to be the lowest since November. Analysts and traders anticipated decent demand at the final Treasuries auction of the week following average bidding at the two-year and five-year note sales. The U.S. Treasury will release the results of the seven-year auction shortly after 1 p.m. (1700 GMT). Longer-dated bond prices were also bogged down by the absence of the Fed, which was not scheduled to buy government debt for its bond program, known as QE3, which is aimed at supporting the U.S. economy.