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* European shares gain 0.62%
* Germany's DAX outperforms after one-day holiday
* German carmarkers shine; tariff-sensitive auto sector up 1.9%
* Dollar firm near 2-1/2 month lows
* Graphic: World FX rates in 2019 http://tmsnrt.rs/2egbfVh
LONDON, June 11 (Reuters) - European shares gained ground on Tuesday, with Germany's carmakers outperforming, as risk appetite held firm after the United States stepped back from imposing tariffs on Mexico.
The pan-European STOXX 600 climbed 0.62%, on course for a sixth day of gains in the last seven, with Frankfurt's DAX racing up 1.2% as German investors returned from a one-day holiday.
There, BMW, Daimler and VW - seen as sensitive to trade tariffs - all gained between 1.8%-2%, mirroring a 1.9% gain for the auto sector.
Investors have breathed easier this week after the United States and Mexico reached a deal on Friday to avert tariffs threatened by U.S. President Donald Trump if steps were not taken to curb the flow of mostly Central American migrants.
That eased - for now at least - fears that the United States would find itself in a trade war with another of its largest commercial partners, adding to the dispute with China.
Trump said on Monday he may impose more tariffs on Chinese imports if he cannot make progress in talks with President Xi Jingping at a Group of 20 summit in Japan later this month.
Market participants said that investors would have to wait until the G20 summit, scheduled for June 28-29, for clear signs of how the spat would play out.
In the meantime, stocks are likely to be buoyed by expectations of a cut in rates by the U.S. Federal Reserve. Markets have priced in a cut by July.
"It looks like we will have to wait to see at the end of the month, to see what the next move will be," said David Madden, an analyst at CMC Markets. "In that time, if nothing is said, stocks could press on higher the belief that the Fed will all of a sudden become dovish is really driving markets."
The MSCI world equity index, which tracks shares in 47 countries, advanced 0.24%. Wall Street futures were also seen opening higher, with S&P500 mini futures up 0.26%.
In Asia, MSCI's broadest index of Asia-Pacific shares outside Japan gained 0.9%, with Shanghai's bourse climbing 2% after China tweaked policy on major investment projects in an attempt to support its slowing economy.
Bourses in Australia, South Korea and Japan also gained.
The dollar held steady above a 2-1/2 month low against a basket of currencies, with rising expectations for a Fed rate cut tempered by a reluctance to close positions before the G20.
The dollar index nudged down 0.03% to 96.747 after advancing 0.2% on Monday.
"The markets are pricing in a 25-basis-point rate cut in July," said Peter Schaffrik, head of European rates strategy at RBC Capital Markets, adding that expectations of looser policy would likely continue.
"When you see the narrative that the market is painting, that it is all down to the negative implications from the trade war and the reduction of global trade," he said. "It's difficult to see how any one data point will change the entire picture."
Amid the cautious optimism, a rally in longer-dated euro zone government bonds stalled as the pick-up in risk sentiment globally sparked a sell-off in the bloc.
Germany's 10-year bond yield, seen as a benchmark for government debt, was up 3 basis points at minus 0.23% - still a smidgeon away from last week's record lows.
Thirty-year bond yields in Germany and France were up as much as 8 basis points in early trade.
In commodities, oil prices rose, bolstered by firmer financial markets and expectations that producer group OPEC and its allies will keep withholding supply. Brent crude futures were at $62.67 at 0741 GMT, up 0.4%.
For Reuters Live Markets blog on European and UK stock markets, please click on: (Reporting by Tom Wilson; Editing by Andrew Cawthorne)