* S&P 500 clears 3,000 hurdle
* China central bank says to strengthen economic policy
* Oil gains as supply falls, U.S. rigs hit all-time low
* World FX rates in 2020 http://tmsnrt.rs/2egbfVh
By Herbert Lash and Marc Jones
NEW YORK/LONDON, May 26 (Reuters) - Global equity markets strode higher on Tuesday, along with crude oil, as investors set aside Sino-U.S. rhetoric to focus on more stimulus in China and the prospect of a reopening world economy.
The euro got a boost from a weaker dollar as growing optimism about a global economic recovery from the COVID-19 pandemic supported riskier currencies and sent safe-haven gold lower.
Crude prices rose, supported by growing confidence that producers are following through on commitments to cut supplies and as fuel demand picks up as coronavirus lockdowns ease.
MSCI's gauge of stock performance in 49 countries surged more than 2%, as did its emerging markets index, while the S&P 500 climbed past the 3,000 mark, up 37% from March lows but still off about 11% from its all-time high in February.
Europe was powered by a 6.6% surge in travel and leisure stocks .SXTP while share of U.S.-listed cruise ship operators jumped more than 11%.
The major driver of positive investor sentiment is the reopening of the U.S. and global economies, said Jason Benowitz, senior portfolio manager at the Roosevelt Investment Group Inc. in New York.
"Reports of economic activity, while still terrible compared to three months ago, have begun to get less bad as compared to the prior month. This suggests the economy has bottomed and may be starting to rebound off its lows," Benowitz said.
Shares related to the travel industry led gainers in Europe and on Wall Street. Spain said quarantine-free tourism would resume next month and Germany edged toward a 9 billion-euro bailout of airline Lufthansa. Melia Hotels International SA MEL.MC and France's Accor SA ACCP.PA both rose more than 12%, leading the Spanish and French bourses. Norwegian Cruise Line Holdings Ltd . NCLH.K , Carnival Corp CCL and Royal Caribbean Cruises Ltd. RCL.N were among the top five gainers on the S&P 500.
The travel industry remained vulnerable. Latin America's largest airline, LATAM Airlines Group LTM.SN and its affiliates in Chile, Peru, Colombia and Ecuador filed for bankruptcy protection in the United States.
MSCI's all-country world index .MIWD00000PUS gained 1.92%, and the pan-European STOXX 600 index .STOXX rose 1.16%.
The Dow Jones Industrial Average .DJI rose 621.07 points, or 2.54%, to 25,086.23. The S&P 500 .SPX gained 53.45 points, or 1.81%, to 3,008.9 and the Nasdaq Composite .IXIC added 82.98 points, or 0.89%, to 9,407.57.
While some investors believe equities are getting ahead of valuations, with economic conditions worse than the last time the S&P 500 advanced past 3,000 and a potential resurgence in COVID-19 cases, stock prices are forward-looking, Benowitz said.
"It seems likely that the economic recovery will not be smooth," he said. "We also expect growth to resume and corporate earnings to advance well off their lows in the next few years."
Crude prices were buoyed by Russia saying its oil output had dropped close to its target of 8.5 million bpd for May and June under the supply deal reached by major producers. LCOc1 was at $35.59 a barrel, up 0.17% on the day. U.S. crude CLc1 recently rose 1.62% to $33.79 a barrel.
China's central bank said it would continue to push to lower interest rates on loans, helping offset tensions between Beijing and Washington over trade, the coronavirus and Chinese proposals for stricter security laws in Hong Kong. broadest index of Asia-Pacific shares outside Japan .MIAPJ0000PUS advanced 1.7% overnight, with South Korea .KS11 up 1.75% and Chinese blue chips .CSI300 1.1% higher.
The dollar index =USD fell 0.699%, with the euro EUR= up 0.72% to $1.0977.
The Japanese yen JPY= strengthened 0.08% versus the greenback at 107.62 per dollar.
Benchmark U.S. 10-year Treasury notes US10YT=RR rose 4.1 basis points to yield 0.7063%.
Spot gold XAU= dropped 1.0% to $1,711.73 an ounce.
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