* Dollar pulls back after 3-year high vs currency basket * European shares gain 1.6 pct, Wall Street stocks higher * Oil pulls back after gains on Egypt By Caroline Valetkevitch NEW YORK, July 8 (Reuters) - Global stock indexes rose on Monday after last week's stronger-than-expected U.S. jobs report while the dollar pulled back after hitting a three-year high against a basket of currencies. Brent crude oil eased after rising sharply on unrest in Egypt, which stoked concerns about global oil supplies. Friday's upbeat U.S. jobs data supported views that the U.S. labor market recovery was gaining steam but also fueled concern the Federal Reserve could soon start reducing its $85 billion a month stimulus. In contrast, the European Central Bank and the Bank of England were more likely to ease monetary policy, while the Bank of Japan was expected to continue with aggressive stimulus, keeping the euro, sterling and the yen weak. In early New York trade, the dollar index was down 0.3 percent at 84.222, having hit 84.588 earlier, its strongest since July 2010. On Wall Street, the Dow Jones industrial average was up 93.58 points, or 0.62 percent, at 15,229.42. The Standard & Poor's 500 Index was up 9.50 points, or 0.58 percent, at 1,641.39. The Nasdaq Composite Index was up 4.99 points, or 0.14 percent, at 3,484.37. MSCI's global share index was up 0.5 percent. "Any shift lower from here would not necessarily be a vote of no confidence or a vote of caution for the market," said Peter Kenny, chief market strategist at Knight Capital in Jersey City, New Jersey. Europe's broad FTSEurofirst 300 stock index was up 1.5 percent. Investor focus was also on Brussels, where Greece was expected to reach a deal over its latest aid payment at a meeting of euro zone finance ministers later in the day, and there was relief after weekend moves to calm Portugal's political crisis. BOND PRICES RISE U.S. Treasuries prices climbed on buying by bargain-minded investors, helping to bring benchmark yields down from near two-year highs. A Reuters poll conducted after the release of Friday's government payrolls data -- in which U.S. employers added 195,000 jobs in June -- showed more than half of the major Wall Street bond firms surveyed expected the Fed would reduce its $85 billion monthly purchases of Treasuries and mortgage-backed securities in September. The 10-year Treasury note last traded 19/32 higher in price to yield 2.6622 percent. "Today we are trying to find a range before this week's supply. Some people are thinking maybe Friday was overdone," said Thomas Roth, executive director of U.S. government bond trading at Mitsubishi UFJ Securities USA in New York. The divergence between the United States and other major economies is clear in bond markets, with 10-year Treasury yields spiking 23 basis points on Friday to around 2.75 percent, highs last seen in August 2011. The spread between Treasury and bund yields gapped to the widest since 2006. The U.S. Treasury Department will sell $32 billion of three-year notes on Tuesday; $21 billion of 10-year notes on Wednesday and $13 billion of 30-year bonds on Thursday. Brent, the European benchmark, eased 37 cents to $107.35 a barrel, after hitting $108.04, the highest since April 4, while U.S. light crude was down 26 cents at $102.96.