* 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, updates prices) By Gertrude Chavez-Dreyfuss NEW YORK, Oct 8 (Reuters) - U.S. Treasury yields retreated on Thursday, with those on long-dated debt falling from four-month peaks hit earlier this week, amid persistent uncertainty about the stimulus talks on coronavirus aid. The yield 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 on expectations of growth and inflation given the U.S. stimulus to combat the virus" negative impact. U.S. yields, however, inched higher after a soft 30-year bond auction. The high yield for the auction was 1.578%, above market expectations at the bid deadline. The bid-to-cover ratio, a measure of demand, was at 2.29, slightly below the 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 restarted over further COVID-19 relief and cited 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 said on Thursday, however, there would be no additional federal aid for U.S. airlines without a more comprehensive COVID-19 relief package, adding she was hopeful for a larger deal "because it has to be done." Pelosi"s comments pushed U.S. 10-year and 30-year yields to session lows. Trump had pushed late on Tuesday for a targeted aid package for airlines, individuals and small businesses. "It"s overall general uncertainty. It"s a very shaky environment," said Kim Rupert, managing director of global fixed income analysis at Action Economics in San Francisco, explaining the fall in yields. Rupert said she did not believe Republicans would go for Pelosi"s broad stimulus plan, because it had too many non-COVID provisions. "We"re so close to the elections now that I don"t think there"s room to compromise." In late 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 1.569%, 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 0.146% from Wednesday"s 0.157%. The spread between five-year and 30-year yields also shrank to 123.50 basis points. With auctions out of the way, market participants are looking to see whether the yield curve"s steepening trend will continue. "We know the Federal Reserve is sitting on rates so we don"t think rates are going to go very high," said Action"s Rupert. "The Fed continues to expect tame inflation so that"s also limiting the upside in yields." October 8 Thursday 3:11PM New York / 1911 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 99-245/256 0.1468 -0.010 Three-year note 99-206/256 0.1903 -0.013 Five-year note 99-158/256 0.3276 -0.017 Seven-year note 98-224/256 0.5396 -0.018 10-year note 98-164/256 0.7685 -0.017 20-year bond 96-100/256 1.3325 -0.021 30-year bond 95-100/256 1.569 -0.020 DOLLAR SWAP SPREADS Last (bps) Net Change (bps) U.S. 2-year dollar swap 8.75 0.50 spread U.S. 3-year dollar swap 8.00 0.75 spread U.S. 5-year dollar swap 7.75 0.75 spread U.S. 10-year dollar swap 3.00 0.75 spread U.S. 30-year dollar swap -35.25 1.25 spread (Reporting by Gertrude Chavez-Dreyfuss Editing by Nick Zieminski and Richard Chang)