(Refiles to include additional subscribers, no changes to text) LONDON, Sept 28 (Reuters) - U.S. Treasuries extended their selloff into a fourth day on Tuesday, with 10-year yields rising to new end-of-June highs while the TIPS market also started pricing in higher future inflation. The prospect of rising cash rates and the risk of inflation proving less transitory than expected took two-year yields to 18-month highs. The selloff gathered pace during European trade, with yields across the U.S. curve as much as 7.5 basis points higher on the day. European bond yields soared too. Two-year yields at 0.3167% have roughly doubled since June, when the U.S. Federal Reserve surprised markets by beginning to project rate hikes for 2023. “It validates a more hawkish dot plot, and it’s building on what’s already baked in,” Vishnu Varathan, head of economics at Mizuho in Singapore, said, referring to the Fed’s rate projections, which now show a hike in 2022. On Monday, the U.S. government had to double the coupon on new notes to 0.25% to reflect market pricing of higher overnight rates for the next two years. The move also reflects the impending rollover of the two-year future to the December contract, which implies a yield around 0.35%. Monday data showing a surge in U.S. firms’ capital goods orders last month could tilt policymakers in favour of lifting rates sooner rather than later, Varathan added. Five-year Treasuries were also under pressure, and the yield, which rises when prices fall, crossed 1% for the first time since February 2020. It has surged 17 basis points in five sessions and last sat at 1.04%. Benchmark 10-year yields meanwhile jumped almost 7 bps to 1.55%, their highest since June. They have risen almost 25 bps in September and are set for their biggest monthly jump since March. Growing inflationary pressures are starting to make investors nervous, with oil at three-year highs and Fed chair Jerome Powell flagging that price pressure as a result of reopening bottlenecks might be stickier than first thought. The yield on the 10-year U.S. Treasury Inflation-Protected Securities (TIPS) rose to -0.82%, its highest since late June. That move pushed up the inflation breakeven rate by around 4 bps in another sign of rising inflation expectations. Breakevens remain below this year’s highs hit in March, however. “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,” Martin Whetton, head of fixed income at Commonwealth Bank in Sydney, said. Reporting by Tom Westbrook in Singapore, additional reporting by Sujata Rao and Dhara Ranasinghe in London Editing by Sherry Jacob-Phillips and Susan Fenton Our Standards: The Thomson Reuters Trust Principles.