* Dollar set for more gains on Fed outlook, economy * Euro falls on comments from ECB's Asmussen, Italy ratings cut * Sterling hits three-year low vs dollar after weak UK data By Wanfeng Zhou NEW YORK, July 9 (Reuters) - The U.S. dollar rallied to three-year highs against major currencies on Tuesday, extending a bullish run on expectations the Federal Reserve will reduce stimulus at a time when other major central banks are likely to ease further. The euro hit a three-month low against the dollar after Standard & Poor's cut Italy's sovereign credit rating and European Central Bank policymaker Joerg Asmussen told Reuters Insider TV that the bank's guidance on interest rates staying at record lows extends beyond 12 months. "Diverging expectations for global central bank policy have been at the heart of the dollar's rise," said Joe Manimbo, senior market analyst at Western Union Business Solutions in Washington. The dollar index, which measures the greenback against a basket of six currencies, rose as high as 84.753, the strongest since July 2010. It last traded at 84.608, up 0.5 percent on the day. The euro fell as low as $1.2754, according to Reuters data, its lowest since early April. It last traded down 0.7 percent at $1.2785. Rating agency S&P cut Italy's sovereign credit rating to BBB from BBB-plus on the country's crumbling economy. The outlook remains negative, S&P said in a statement. The ECB said last Thursday it would keep its interest rates at present or lower levels for an "extended period," - its first use of so-called forward guidance, abandoning its traditional policy of never pre-committing on future rates. The ECB later issued a statement in which it said Asmussen had not intended to give any guidance on the exact length of time for which it expects to keep rates at record lows. Expectations the Fed, which releases minutes from its June monetary policy meeting on Wednesday, will start to scale back its $85 billion a month in asset purchases as early as September, have encouraged investors to buy dollars. Fed Chairman Ben Bernanke is also slated to speak on Wednesday. Currency speculators increased their bets in favor of the U.S. dollar to $22.37 billion in the week ended July 2 from $13.28 billion a week ago, according to data from the Commodity Futures Trading Commission released on Monday. Analysts said while U.S. dollar longs increased sharply in the latest week, it was still well below the peak seen in May, suggesting further upside. "This is momentum-driven trade and we are looking for more dollar strength," said Mankash Jain, head of FX and Investment Management at Solo Capital. "Any bounce in the euro toward $1.2950 is a time to initiate fresh short positions." The Bank of England and Bank of Japan are also widely expected to provide more stimulus to boost growth. Sterling fell 0.6 percent to $1.4865 after weak factory output and trade data, which were was seen as raising the risk of the Bank of England easing monetary policy in coming months. It had fallen as low as $1.4812, a three-year trough. "Short sterling/dollar remains a favored trade and our view has long been that U.S.-UK growth differentials are a convincing rationale for further downside," Commerzbank said in a research note. Against the yen, the dollar was flat at 100.99 yen. The euro lost 0.6 percent to 129.10 yen.