(Corrects in second paragraph to clarify that layoffs, not jobless claims, fell to a 21-year-low) * Adds U.S. market open, new commentary, changes dateline, byline; previously LONDON * European stocks near record high as data improves * Dollar hits 15-month peak vs yen, 4-month peak vs euro * Oil consolidates roaring 45% H1 rally * All eyes on Friday’s payrolls data NEW YORK, July 1 (Reuters) - Global stock markets rose on strong European and U.S. shares on Thursday, with stocks brushing off a rapid re-acceleration in coronavirus cases and oil and the dollar extending their first-half rallies. On Wall Street, the S&P 500 index kicked off the second half of the year at record levels after data revealed fewer-than-expected weekly jobless claims. Layoffs also fell to a 21-year low in June. London, Frankfurt, Paris and Milan overcame a midmorning wobble to keep the pan-European STOXX 600 reaching for a record high. In an Asia session thinned by a holiday in Hong Kong, Japan’s Nikkei fell 0.3% and the yen hit a 15-month low as sources in Tokyo said COVID-19 restrictions were likely to be extended. Oil rose almost $2, supported by the prospect of strengthening demand, lower U.S. stockpiles and a Reuters report that OPEC+ producers could increase output in the coming months. The dollar index hit three-month highs, ahead of Friday’s U.S. jobs report that could offer clues on when the Federal Reserve will start to pare back stimulus. “Markets are digesting improved economic data and rising inflation, closely scrutinizing central bank communication for clues regarding the timing, process and magnitude of policy normalization,” said Ben Randl, a senior analyst at Bank of America Merrill Lynch. U.S. government bond prices were lower, with the benchmark 10-year yield last yielding 1.4696%. Germany’s benchmark 10-year Bund yield was up one basis point on the day, at -0.2%. French, Spanish and Italian 10-year yields were up by similar amounts . Gold rose on Thursday in step with a dip in the dollar and Treasury yields, paring some of the precious metal’s losses last month. MSCI’s gauge of stocks across the globe gained 0.13%, and the pan-European STOXX 600 index rose 0.53%. MSCI’s broadest index of Asia-Pacific shares outside Japan closed 0.44% lower. TAIWAN TENSIONS In China overnight, equity markets cheered the centenary of the Communist Party with a small rise, but a nationalist address from President Xi Jinping in Tiananmen Square did little to soothe geopolitical nerves, and the yuan weakened. Xi pledged to complete “reunification” with self-ruled Taiwan and vowed to “smash” any attempts at formal independence. Slower vaccination rates in Asia and the extension of restrictions to curb the spread of the virus - as well as a regulatory crackdown on Chinese tech giants - have had regional markets lagging this year. The MSCI ex-Japan index closed out the first half with a gain of 5.8% compared with world stocks’ rise of 11.4% and a gain of 14.4% for the S&P 500, which had logged its fifth consecutive record as it closed out H1 on Wednesday. However, it is U.S. payrolls on Friday that traders think could jolt markets from a slumber that has locked currencies in some of their tightest trading ranges for decades. Initial claims for state unemployment benefits dropped 51,000 to a seasonally adjusted 364,000 for the week ended June 26, the Labor Department said on Thursday, although they are an unreliable guide to Friday’s broader indicators. June had been the best month for the dollar since Donald Trump was elected U.S. president in November 2016, MUFG’s currency analyst Lee Hardman said. “The key trigger,” he said “has been the hawkish shift in the Fed’s policy stance. The more hawkish guidance has left market participants less confident that the Fed will maintain loose policy in the coming years.” The Dow Jones Industrial Average rose 56.14 points, or 0.16%, the S&P 500 gained 12.08 points, or 0.28%, to 4,309.58 and the Nasdaq Composite added 13.74 points, or 0.09%, to 14,517.69. The U.S. dollar index, which measures the greenback against a basket of six major currencies, rose 0.055%, with the euro up 0.06% to $1.1862. Brent crude was last up $1.20, or 1.61%, at $75.82 a barrel. U.S. crude was last up $1.71, or up 2.33%, at $75.18 per barrel. Spot gold prices rose $4.1619 or 0.24 percent, to $1,773.96 an ounce. Reporting by Elizabeth Dilts Marshall in New York and Marc Jones in London; editing by Jonathan Oatis Our Standards: The Thomson Reuters Trust Principles.