* U.S. S&P futures down 0.13% * Euro zone inflation eases in June * European stocks fall 0.89% * U.S. June private payrolls data due LONDON, June 30 (Reuters) - U.S. index futures and European stocks weakened on Wednesday and world shares drew back from recent record peaks, as markets grew jittery about the pandemic again ahead of the half-year-end and key U.S. jobs data later this week. Asset markets have been buoyed over the past year by trillions of dollars of monetary and fiscal stimulus by central banks and governments around the world in response to COVID-19, while vaccination roll-outs in recent months are boosting the economic outlook. “The search for yield is a very powerful force. It doesn’t have the narrative right now to stop it,” said Sebastien Galy, senior macro strategist at Nordea Asset Management. But stocks trimmed some gains on the last trading day of the month and half-year, amid concerns about the more infectious coronavirus Delta variant first identified in India. “At the end of the month there may be some re-balancing going on,” said Giuseppe Sersale, fund manager at Anthilia in Milan. “My impression is that there is a fear for the impact of the Delta variant on the summer season in Europe.” Indonesia, Malaysia, Thailand and Australia are all battling pandemic outbreaks and tightening restrictions, and Spain and Portugal announced restrictions for unvaccinated British tourists. U.S. S&P futures dipped 0.13% after buoyant overnight U.S. share trading as U.S. consumer confidence jumped to its highest level in nearly 1-1/2 years in June. Growing labour market optimism as the economy reopens offset concerns about higher inflation. But European stocks suffered steeper losses, falling 0.89%. German stocks dropped 1.4% and British shares fell 0.67%. The European benchmark, which hit record highs this month, remains on course, however, to post its biggest first-half percentage gain since 1998. Euro zone inflation eased in June in line with forecasts but is expected to move well above the European Central Bank’s target towards the autumn on higher commodity prices. Germany’s 10-year government bond yield fell 2.2 basis points on the data to -0.194%. MSCI’s global share index fell 0.18% but was set for a fifth straight month of gains, a day after hitting an all-time high, and for a rise of more than 11% in the first half. EYES ON PAYROLLS Markets are focusing on U.S. private payrolls data later on Wednesday, ahead of Friday’s release of U.S. non-farm payrolls data which could influence Federal Reserve policy. Economists polled by Reuters forecast Wednesday’s private payrolls showing a gain of 600,000 in June, a slowdown from a month ago when 987,000 jobs were created. For the more comprehensive labour figures on Friday, economists polled by Reuters were expecting a gain of 690,000 jobs for June, up from 559,000 in May. But the variation among the 63 estimates was large, ranging from 400,000 to more than a million. The benchmark 10-year U.S. Treasury note yield fell more than 2 basis points to 1.4528%. The dollar was headed for its best monthly rise since March, mostly in the wake of a surprisingly hawkish shift in the Fed’s rates outlook. A “very optimistic” Fed Governor Christopher Waller on Tuesday said it may need to start dialling down its massive asset purchase programme as soon as this year to allow the option of raising interest rates by late 2022. The dollar index rose 0.06% to 92.123, with the yen steady at 110.49 and the euro down 0.1% at $1.1882. Sterling was up 0.17% at $1.3859. MSCI’s index tracking Asian shares outside Japan was set for a small monthly loss, but still on course for a fifth straight quarterly rise, its longest such streak since 2006-2007. The index slipped 0.05%. Chinese blue chips added 0.65%. Japan’s Nikkei was down 0.07%. Oil prices were heading for monthly and quarterly gains after some data suggested U.S. crude stockpiles were shrinking. Brent crude rose 0.78% to $75.34 per barrel and U.S. crude jumped 1% to $73.93. Spot gold lost 0.14% to $1,759.36 an ounce, putting it on course for its biggest monthly drop since November 2016. Additional reporting by Danilo Masoni in Milan and Andrew Galbraith in Shanghai; Editing by John Stonestreet, Alex Richardson, Philippa Fletcher Our Standards: The Thomson Reuters Trust Principles.