* Dollar tumbles 1.2 percent after dovish Bernanke * European shares rise almost 1 percent, Asian stocks gain * German Bunds track U.S. Treasuries higher * Commodities from oil to copper see gains By Marc Jones LONDON, July 11 (Reuters) - Shares and bonds rallied globally on Thursday and the dollar tumbled after the head of the U.S. central bank signalled it may not be as close to winding down its stimulus policy as markets had begun to think. Fed Chairman Ben Bernanke said on Wednesday the overall message coming from the central bank was that "a highly accommodative policy is needed for the foreseeable future." Despite minutes from the Fed's June meeting showing half of its policymakers think its $85 billion-a-month stimulus programme should be wound down by the end of the year, his message was enough to snap markets back into buying mode. European bonds from Germany to Greece tracked gains in U.S. debt and European shares climbed almost 1 percent to push MSCI's world index to its highest in almost a month. "Bernanke's comments were taken by the markets as much more dovish so I suspect it will be a good day for risk markets," said Saxo bank Chairman and senior market analyst Nick Beecroft. "We are still in a bit of a sweet spot for equity markets. The economy is doing well enough to encourage equity markets about future earnings, but not too hot to cause the Fed to remove accommodation." The dollar, which had touched three-year highs before Wednesday's Fed remarks, tumbled 1.2 percent against a basket of major currencies, while the euro roared to a three-week high of $1.32085 before easing to $1.3042 by 0920 GMT. The big stock and bond swings over the last few weeks have highlighted the tricky task the Fed and other central banks have as they try and wean markets off the cheap and easy money they have provided during the global financial crisis. "Communication is a real challenge for the Fed so brace for further whipsaws on Bernanke's semi-annual testimony (next week)," said Sean Callow, a currency strategist at Westpac. HSBC currency analyst Daragh Maher said there had actually been very little difference in Bernanke's wording compared with last month's Fed press conference, and that the volatility was down to markets' habit of overreacting. "The things he said were almost exactly the same... A mixed emphasis from the market is what we are really seeing rather than it being a mixed message from the Fed." EMERGING RELIEF Relief was also evident in emerging markets, some of the hardest hit by the idea of a change in tack in global monetary policy, with emerging equities and currencies rising including the recently-battered Turkish lira. Commodity markets took a boost from the prospect of sustained support by the Fed, along with European and Japanese central banks, supporting global economic growth. Copper prices gained 3.2 percent to exceed $7,000 a tonne, hitting a three-week high. Gold climbed 2.7 percent to a three-week high and was on track for a fourth straight day of gains while U.S. crude oil prices added 0.7 percent to their highest level since March 2012. Commodity currencies also jumped, with the Australian dollar climbing as high as $0.9306, further off a 34-month trough of $0.9036 plumbed just last week. It was helped by a surprise increase in Australian employment in June, which may lessen any near-term risk of more interest rates cuts. But as the yen strengthened, Tokyo's Nikkei share average underperformed other Asian markets, up 0.4 percent. The Bank of Japan kept monetary policy steady at its latest meeting but said an economic recovery was underway, its most optimistic view in 2-1/2 years reflecting the positive impact of a weakening yen and its massive stimulus plan.