UPDATE 1-European shares rise after China's Xi backs away from trade war

* STOXX 600 up 0.8 percent

* Autos rise after China's Xi says to cut import tariffs

* Basic materials, oil and gas jump

* Bayer rallies on reported clearance of Monsanto deal

* LVMH hits record after solid update (For a live blog on European stocks, type LIVE/ in an Eikon news window)

MILAN/LONDON, April 10 (Reuters) - European shares rose on Tuesday after Chinese President Xi Jinping promised to cut import tariffs, fuelling optimism that a trade war between his country and the U.S. could be averted.

Gains were widespread, with the STOXX 600 closing up 0.82 percent, slightly below Wall Street, where the S&P 500 was up 1.8 percent in morning trading.

Xi promised to open China's economy further and lower import tariffs on products including cars, which helped the auto index jump about 1.9 percent.

"We would see this as a major step towards opening the Chinese economy and to easing the very tense trade atmosphere ... The primary beneficiaries would be German carmakers and the German economy as a whole," Evercore ISI analysts wrote.

Germany's BMW rose 1.9 percent and Daimler was up 1.2 percent, while Volkswagen surged 4.5 percent.

Volkswagen carmaker is reported to be seeking to replace Chief Executive Matthias Mueller with the head of its core brand, Herbert Diess, as part of a broader overhaul of its management structure to boost efficiency.

The basic resources index gained the most, rising 2.7 percent, as it also recovered from large losses on Monday when stocks exposed to Russia were hit after the United States announced fresh sanctions.

Higher-than-expected quarterly revenues at Oslo-listed TGS Nopec, a key supplier to the oil industry, boosted its share price, which soared more than 15 percent. The oil and gas sector gained overall as oil hit $70 a barrel on Tuesday, in its biggest two-day rally in nearly a month.

New developments in mergers and acquisitions also moved shares.

French payments firm Ingenico rose 7.1 percent after U.S. competitor Verifone agreed to be taken private for $2.58 billion in cash by Francisco.

Bayer rose 4.7 percent after the WSJ reported that the U.S. Justice Department would allow the German drugs and pesticides group to acquire Monsanto in a $62.5 billion deal, after the companies agreed to sell more assets to win antitrust approval.

LVMH rose 4.9 percent to record highs after the Louis Vuitton owner posted better-than-expected sales growth in the first quarter, helped by thriving Chinese demand for luxury goods. Its solid update boosted shares in other luxury companies such as Kering, up 3.2 percent. (Reporting by Danilo Masoni, editing by Larry King)