* Euro zone periphery govt bond yields tmsnrt.rs/2ii2Bqr (Adds quotes, updates prices) July 8 (Reuters) - Euro zone bond yields fell further on Thursday as a global bond rally continued unabated and the ECB tweaking its inflation target was broadly seen strengthening the central bank’s ultra-easy monetary policy stance. A breakneck rally in U.S. government bonds brought 10-year Treasury yields to a session low of 1.25%, their lowest levels since early 2021 as investors sensed cracks in the economic recovery and the cooling risks of high inflation. The market price action in Europe closely mirrored that on the other side of the Atlantic with German 10-year yields, the euro zone benchmark, down at one stage to -0.34%, a steep fall from the -0.15% it stood at only two weeks ago. At 1511 GMT, Germany’s 10-year yields were at -0.315%, down about 3 basis points on the day, while European stock markets sold off, with the pan-European STOXX 600 losing about 2%. Other euro zone government bonds saw their yields fall, with France’s 10-year flirting with negative returns for some time during the session. While many investors struggle to fully grasp the triggers behind the global bond rally, a broad rethink of the reflation narrative and a sense that economic growth may have peaked are common explanations, together with hedge funds unwinding bets gone wrong. U.S. data showed on Thursday that the number of Americans filing new claims for unemployment benefits rose slightly, another indication that the labor market recovery from the COVID-19 pandemic continues to be choppy. Amid markets adjusting to prices rising slower than previously anticipated, the European Central Bank, in a widely expected decision, set its inflation target at 2% in the medium term, ditching a previous formulation for “below but close to 2%”. The adoption of the symmetrical inflation target - where a central bank responds to inflation undershoots as well as overshoots – had little impact on euro area borrowing costs, which are pinned down by the ECB’s monetary support. “It was already clear what they were going to do,” Arne Petimezas, analyst at AFS in Amsterdam, said of the lack of market reaction. Overall analysts broadly took the view that the central bank would continue to provide stimulus well into the recovery. “Looking ahead, this decision will provide further support for the ECB to continue its ultra-dovish tone and supporting the eurozone with favourable financing conditions,” said Jesús Cabra Guisasola, Associate at Validus Risk Management. In addition to the revision of its inflation target, the ECB will also incorporate climate change considerations into its monetary policy, including on disclosure, risk assessment, and decisions on collateral and corporate sector asset purchases. (Reporting by Yoruk Bahceli, Julien Ponthus and Carolyn Cohn; Editing by Angus MacSwan, Raissa Kasolowsky and Sonya Hepinstall) Our Standards: The Thomson Reuters Trust Principles.