* European shares climb to highest since early March
* German DAX plays catch up after day off
* U.S. unrest and Sino-U.S. worries rumble in background
* Dollar nurses losses after Monday tumble
By Marc Jones
LONDON, June 2 (Reuters) - World stocks climbed towards three-month highs on Tuesday as the global coronavirus recovery effort won out over U.S.-China tensions and the worst civil unrest in the United States in decades.
U.S. President Donald Trump's vow to use force to end violent protests in American cities and reports China had ordered U.S. soybean purchases to be halted had checked Asia overnight, but Europe got the bulls back on track.
The pan-European STOXX 600 jumped over 1%. Germany's DAX surged nearly 3% on news Lufthansa's board had approved its government bailout and as Volkswagen and BMW shares rose as much as 7% at the prospect of a 5 billion- euro government-funded scheme to boost sales.
The euro was at a two-and-a-half-month high as the dollar struggled. Italian and Spanish bonds were still being helped by a proposed 750 billion-euro EU stimulus plan and bets on more European Central Bank help.
"In a way, it is remarkable that the market remains in this positive mood," said Elwin de Groot, head of macro strategy at Rabobank. "Even with these rising protests in the U.S. and the situation in Hong Kong at the moment, the market is pushing on and seeing room for optimism."
World stock markets have rallied nearly 36% from March lows on hopes for a swift recovery from a pandemic that has killed nearly 375,000 people and crushed global growth as countries shut down to try and slow the virus' spread.
May Purchasing Managers Index data pointed to a fragile but encouraging recovery in global manufacturing, raising hopes that the worst is over.
Japan's Nikkei rose 1.2% to its highest since late February in Asia and markets in Seoul, Taipei and Hong Kong also gained.
"This optimistic read for risk can only persist if measures like orders and employment continue to improve month to month," said Alan Ruskin, chief international strategist at Deutsche Bank.
"Early setbacks would be a very poor sign, but are not expected in the period immediately following the end of lockdowns."
The dollar was at multi-month lows against most major currencies following a 5% drop for its main index in recent weeks.
The euro got as high as $1.1160 on Tuesday, Britain's pound topped $1.2530 for the first time in over a month and the Canadian and Australian dollars both rose around 0.4% as commodity markets continued their recoveries.
Brent oil rose another 2% to just over $39 a barrel. Traders are expecting major producers to extend output cuts at an OPEC+ meeting later in the week. U.S. crude was up 1% at $35.86 a barrel.
Copper prices were at their highest in nearly three months on signs that demand from top metals consumer China was recovering.
Stockpiles CU-STX-SGH dropped at the fastest pace last week since September 2017, data showed. Aluminum producer Rusal said its customers were gradually returning after a major slump in April.
"This is real demand. Domestic investment is booming，especially in infrastructure. Supply and transport slowdowns from South America are also supporting prices," said a copper trader in China.
Additional Reporting by Mai Nguyen and Tom Westbrook in Singapore; editing by Larry King