(Updates yields, adds analyst comments, upcoming auction, yield curves) Sept 28 (Reuters) - U.S. Treasuries extended their sell-off into a fourth day on Tuesday with the 10-year yield reaching a level last seen in mid-June, while inflation expectations rose. The benchmark 10-year yield, which climbed as high as 1.567%, was last up 5.7 basis points at 1.5409% and was heading for its biggest monthly rise since March. Yields on two- and five-year notes jumped to their highest levels since the first quarter of 2020. Prices, which move inversely to yields, continued to be pulled down after the U.S. Federal Reserve last week revealed its latest clues on tapering its asset purchases and hiking interest rates, according to Kim Rupert, managing director of global fixed income analysis at Action Economics. She added that uncertainty in Washington over this week"s government funding deadline, the debt ceiling limit and the potential for more massive federal spending also weighed on the market. "It"s just so uncertain that it"s leaving bulls kind of sidelined so no one wants to get in the mix with all of that going on," Rupert said. Growing inflationary pressures are starting to make investors nervous, with oil at three-year highs and Fed Chair Jerome Powell flagging that price pressures as a result of reopening bottlenecks might be stickier than first thought. The yield on 10-year U.S. Treasury Inflation-Protected Securities rose to its highest since late June and was last at -0.850%. Inflation expectations also climbed, with the breakeven rate rising to 2.407%, which was below the year"s high of 2.564% reached in May. "The market is thinking that some of the inflation is a little bit less transitory... and so longer bond investors want a bit more compensation," said Martin Whetton, head of fixed income at Commonwealth Bank in Sydney. Later on Tuesday, the U.S. Treasury will auction $62 billion of seven-year notes. Rupert said the offering comes after mixed results from Monday"s auctions of two- and five-year notes. "If this debt limit mess makes foreign investors skittish, then we"ll probably see a not-too-great auction," she said. "But again, the way things have cheapened up, maybe it goes OK and it"s also month end quarter end coming up, so that might provide a little bit of underpinning." A closely watched part of the yield curve that measures the gap between yields on two- and 10-year Treasury notes was last 2.31 basis points steeper at 123.21 basis points. The yield curve between five-year notes and 30-year bonds also steepened and was last at 105.40 basis points. September 28 Tuesday 10:21AM New York / 1421 GMT Price Current Net Yield % Change (bps) Three-month bills 0.04 0.0406 0.003 Six-month bills 0.0525 0.0532 0.002 Two-year note 99-227/256 0.3069 -0.002 Three-year note 99-118/256 0.5588 0.006 Five-year note 99-76/256 1.0196 0.022 Seven-year note 98-160/256 1.3336 0.041 10-year note 97-88/256 1.5409 0.057 20-year bond 95-116/256 2.0291 0.084 30-year bond 98-56/256 2.0803 0.085 DOLLAR SWAP SPREADS Last (bps) Net Change (bps) U.S. 2-year dollar swap 9.25 -2.00 spread U.S. 3-year dollar swap 13.00 0.50 spread U.S. 5-year dollar swap 8.75 -0.75 spread U.S. 10-year dollar swap 3.00 0.50 spread U.S. 30-year dollar swap -24.00 0.25 spread (Reporting by Karen Pierog in Chicago and Tom Westbrook in Singapore, additional reporting by Sujata Rao and Dhara Ranasinghe in London Editing by Sherry Jacob-Phillips, Susan Fenton and Dan Grebler) Our Standards: The Thomson Reuters Trust Principles.