* MSCI World Index up 0.3%; Brent above $70/bbl * Dollar down 0.1%, gold up; US 10-year up 2 bps * Graphic: Global asset performance tmsnrt.rs/2yaDPgn LONDON/SINGAPORE, June 1 (Reuters) - Global stocks again hit record highs and oil rose on Tuesday, before European and U.S. data that should this week offer major clues on the health of the world economy. Risk markets have eked out gains in recent weeks as traders balance optimism that the United States and other key markets are reopening after pandemic-induced lockdowns with concern that rising inflation could prompt central banks to rein in stimulus programmes. The recovery from COVID-19 also remains patchy in many parts of the world, with exports reviving but broader economic activity still dampened by measures to contain fresh outbreaks. Against that backdrop, euro zone inflation numbers on Tuesday will give an indication of rising pressures in the bloc, while Friday’s U.S. jobs data should give a firmer steer on near-term Fed policy action. In advance of that, MSCI’s broadest gauge of global stock markets rose 0.3% to a record high, led by broad gains across Europe’s leading indexes, with the STOXX Europe 600 up 0.7%. Overnight, MSCI’s broadest index of Asia-Pacific shares outside Japan rose 0.6%, hitting the highest in a month and taking total gains so far this year past 7%. South Korean stocks rose 0.6% after a jump in May exports, and Chinese stocks climbed 0.2% after data showing factory activity expanded at the fastest pace this year in May. This week’s main event is Friday’s U.S. payrolls data, with markets looking for a signal from the Federal Reserve on when it will start tapering its bond-buying programme. Median forecasts are that 650,000 jobs were added in May, but the outcome is uncertain following April’s unexpectedly weak 266,000 gain. Though U.S. inflation data last week was above estimates, another big miss on the jobs front would delay prospects for any wind-down of stimulus, analysts say. Societe Generale strategist Sebastien Galy said he expected the jobs data to come in below or in line with consensus, but, given low levels of equity volatility, markets were primed for a jump on higher-than-expected numbers. “We remain constructive on risk as we expect a disappointment on NFP (non-farm payrolls) but the equity volatility market is likely to reprice higher from its rather extreme lows,” he said in a note to clients. As traders awaited clues on Fed direction, the dollar edged down 0.1% against a basket of its major peers and the yield on U.S. 10-year government debt was up 2 basis points. Concerns about global inflation have driven gold up 8% this month to comfortably above $1,900. Oil prices rose ahead of an OPEC+ meeting and on optimism that fuel demand will grow in coming months as the U.S. summer driving season gets under way. Brent crude futures for August added 1.4% to $70.32 a barrel, while U.S. crude rose 2.3% to $67.81. Editing by Sam Holmes and John Stonestreet Our Standards: The Thomson Reuters Trust Principles.