(Adds details, updates prices) Sept 28 (Reuters) - Euro zone bond yields rose to their highest in three months on Tuesday and inflation expectations reached levels last seen in 2015, as markets fretted over leading central banks’ monetary policy outlooks. Government bond yields have been rising since U.S. Federal Reserve policymakers last week projected the central bank would be ready to raise rates in 2022, and said the Fed could begin reducing its monthly bond purchases as soon as November. Similar messaging from the Bank of England has added to the hawkish tone. Surging energy prices and bottlenecks in supply chains have stoked inflation across the world, putting pressure on bond investors and central bankers who have seen the rise so far as transitory. On Tuesday, U.S. 10-year Treasury yields jumped to their highest level since June and several other benchmark yields rose to their highest since the start of the COVID-19 pandemic. Though the European Central Bank is poised to keep monetary policy looser for longer than its peers because of the bloc’s economic outlook, the moves are also pushing up euro zone bond yields, which are closely correlated to U.S. Treasuries. Inflation in the bloc is far above the ECB’s target, and some policymakers are bracing for it to come in above projections - which have already been raised. Germany’s 10-year yield, the benchmark for the bloc, rose to the highest since end June 30 at -0.172% before paring gains. By 1515 GMT it was up 3 bps at -0.198%. Italy’s 10-year yield rose to its highest since end-June and was last up 6 bps at 0.858%. French and Dutch 10-year yields rose to similar milestones. Though nominal yields have risen this week, the fall in euro area real yields, which strip out the impact of anticipated inflation, has outpaced that rise. That has raised breakeven levels - which measure the difference between nominal and real bond yields and are used to gauge market-based inflation expectations. A gauge tracked by the ECB rose to the highest since July 2015 at 1.8332%. It was last at 1.7855%. “It feeds into my theory that (monetary policy) uncertainty is having an impact here... If you’re uncertain for the outlook for inflation, you need additional compensation to go long breakevens,” said Richard McGuire, head of rates strategy at Rabobank in London. “Ordinarily, you would think if central banks are becoming more hawkish, we should be pricing out inflation expectations... but we’re not and I think that combination of events is a clear signal that something else is afoot.” ECB President Christine Lagarde on Tuesday played down inflation fears and promised patience before policy tightening as the bank was determined not to overreact to what it still deems a temporary surge in prices. U.S. Fed Chair Jerome Powell said on Tuesday the U.S. economy is far from achieving maximum employment, a key component of the central bank’s requirements for raising interest rates. In the primary market, the Netherlands raised 4.915 billion euros from the launch of a new bond due 2029 at auction. Reporting by Yoruk Bahceli, additional reporting by Danilo Masoni; editing by Timothy Heritage, Kevin Liffey and Barbara Lewis Our Standards: The Thomson Reuters Trust Principles.