* Trump says COVID-19 aid talks have resumed * Pelosi says no airline deal without broad COVID bill * U.S. jobless claims weaker than expected * U.S. 30-year bond auction outcome on the weak side (Adds new comment, Pelosi remarks on stimulus, 30-year bond auction results, updates prices) By Gertrude Chavez-Dreyfuss NEW YORK, Oct 8 (Reuters) - U.S. Treasury yields retreated on Thursday, with long-dated debt falling from four-month peaks hit earlier this week, amid persistent uncertainty about the stimulus talks on coronavirus aid as well as weaker-than-expected jobless claims data. With yields down for the day, the curve flattened a bit, with the spread between the two-year and 10-year yields at 61.6 basis points. Since late July, though, the curve has steepened by around 30 basis points. U.S. yields, however, inched higher after a soft 30-year bond auction. The high yield for the auction was 1.578%, higher than what market expected at the bid deadline. The bid-to-cover ratio, a measure of demand, was at 2.29, slightly lower than 2.31 last month. Markets, though, were focused on U.S. stimulus discussions. Two days after calling off U.S. stimulus negotiations, President Donald Trump, in an interview with Fox Business Network, said talks with Congress have re-started over further COVID-19 relief and that there was a good chance a deal could be reached. He gave no other details about a possible agreement. Treasury yields inched higher after Trump"s comments, but came back down. U.S. House Speaker Nancy Pelosi on Thursday said there would be no additional federal aid for U.S. airlines without a more comprehensive COVID-19 relief package, adding that she was hopeful for a larger deal "because it has to be done." Trump had pushed late on Tuesday for a targeted aid package for airlines, individuals, and small businesses. "We are trading on stimulus discussions right now," said Jim Vogel, senior rates strategist, at FHN Financial in Memphis, Tennessee. "They move the market quickly, but with no staying power behind the moves." He added that there is very little "immediate, or near-term economic consequences" of whether another stimulus package is approved or not. "That"s true even for industries with the most difficult stretches such as airlines." In early afternoon trading, U.S. 10-year yields fell to 0.766%, from 0.785% late on Wednesday. Ten-year yields rose to their highest level since June on Wednesday. U.S. 10-year yields further slipped after data showed jobless claims totaled 840,000 for the week ended Oct. 3, compared with an upwardly revised 849,000 in the prior week. Yields on U.S. 30-year bonds were at 1.565%, down from 1.589% the previous session. On Tuesday, 30-year yields climbed to a four-month peak. On the short end of the curve, U.S. two-year yields slipped to 0.148%, from Wednesday"s 0.157%. The spread between five-year and 30-year yields also shrank to 123.50 basis points. With the auctions out of the way, market participants are looking to see whether the yield curve"s steepening trend will continue. Rob Robis, chief global fixed income strategist at BCA Research in New York, said a steeper curve typically occurs when there is Treasury issuance. "The primary dealers want to create demand so they kind of lower the price range and so the bonds can be auctioned successfully." "If we get through supply and the curve is still steep, there"s something more going on than just supply." October 8 Thursday 1:52PM New York / 1752 GMT Price Current Net Yield % Change (bps) Three-month bills 0.095 0.0963 -0.003 Six-month bills 0.11 0.1116 0.000 Two-year note 99-244/256 0.1488 -0.008 Three-year note 99-204/256 0.1929 -0.010 Five-year note 99-158/256 0.3276 -0.017 Seven-year note 98-224/256 0.5396 -0.018 10-year note 98-168/256 0.7669 -0.018 20-year bond 96-120/256 1.3279 -0.026 30-year bond 95-128/256 1.5642 -0.025 DOLLAR SWAP SPREADS Last (bps) Net Change (bps) U.S. 2-year dollar swap 8.50 0.25 spread U.S. 3-year dollar swap 7.75 0.50 spread U.S. 5-year dollar swap 7.75 0.75 spread U.S. 10-year dollar swap 2.75 0.50 spread U.S. 30-year dollar swap -35.50 1.00 spread (Reporting by Gertrude Chavez-Dreyfuss Editing by Nick Zieminski)