(Updates throughout) * U.S. weekly jobless claims drop below 400,000; service sector index at record high in May * Indexes: Dow drops 0.03%; S&P sheds 0.30%; Nasdaq nixes 0.86% * Oil prices hold gains; Gold slips * Graphic: World FX rates tmsnrt.rs/2RBWI5E WASHINGTON, June 3 (Reuters) - Global equities markets were little changed on Thursday after stepping back from near-record levels earlier in the week, as investors studied strong U.S. data reports for economic recovery and inflation signals. U.S. stocks pared back some losses on Thursday before shedding those slight gains after reports that President Joe Biden has offered to scrap his proposed corporate tax hike. Oil was little changed following two straight days of gains that took oil futures to highs not seen in a year, after weekly U.S. crude stocks fell sharply while fuel inventories rose more than expected. Gold slid more than 2% as a strengthening labor market helped propel the dollar higher and boosted expectations that the strong economic readings may reignite taper talk from the Federal Reserve. The euro was last down 0.7% at $1.2123, drifting away from highs scaled earlier in the week, while Europe’s broad FTSEurofirst 300 index dropped 0.07 percent to 1,736.44. A better-than-expected U.S. weekly unemployment report and private payrolls numbers for May pointed to strengthening conditions in the labor market, while a measure of service sector activity increased to a record high, pointing to a robust economic rebound. The strong data could force the Federal Reserve to pare back its crisis support sooner than expected, despite central bank officials’ reassurances to the contrary. Yet, wary investors backed away from big bets over concerns of inflation ahead of the Friday release of U.S. jobs data, which should offer further clarity on whether the faster-than-expected pace of economic recovery can be sustained and what that might mean for monetary policy. The MSCI world equity index, which tracks shares in 50 countries, fell 3.85 points or 0.54 percent, to 704.54. The Dow Jones Industrial Average fell 11.4 points, or 0.03%, to 34,588.98, the S&P 500 lost 12.75 points, or 0.30%, to 4,195.37 and the Nasdaq Composite dropped 121.78 points, or 0.89%, to 13,634.55. A surge in euro zone business activity did little to improve sentiment. IHS Markit’s final composite Purchasing Managers’ Index (PMI) jumped to 57.1 last month from April’s 53.8, its highest level since February 2018. The dollar index, which tracks the greenback versus a basket of six other currencies, rose 0.622 points, or 0.69%, to 90.531 after falling 2% in April and a further 1.6% in May. Benchmark 10-year notes last fell 10/32 in price to yield 1.625%, from 1.591%. While broader stock markets remain close to record highs, the momentum seen earlier in the year has ebbed as investors worry a stronger-than-expected rebound from COVID-19 means higher inflation and sooner-than-expected monetary policy tightening. Thursday’s weekly U.S. unemployment claims report will be followed by monthly jobs numbers on Friday. Investors will be looking for signs of an economic rebound and rising inflation. So far though, “increases in inflation expectations have coincided with equities performing well recently,” said Oliver Jones, senior markets analyst at Capital Economics. “In general, we suspect that these conditions will remain in place for a while longer.” Capital Economics forecasts that real global output will grow at the fastest rate in nearly 50 years this year. “While it is possible that major central banks eventually have to tighten policy faster than is widely expected if inflation does not fall back in the way they are anticipating, it will be hard to tell if this is happening until next year at the earliest,” Jones said. Reporting by Katanga Johnson in Washington; Editing by Steve Orlofsky and Nick Macfie Our Standards: The Thomson Reuters Trust Principles.