* Dollar set for more gains on Fed outlook, economy * Euro tumbles on rate guidance remarks by ECB's Asmussen * Sterling hits three-year low vs dollar after weak UK data * CFTC data suggest more dollar upside By Julie Haviv NEW YORK, July 9 The U.S. dollar hit a three-year high against a basket of currencies on Tuesday, with investors increasingly convinced the Federal Reserve is leaning toward reducing stimulus at a time when other major central banks could opt to further ease monetary policy. The euro, which dominates the composition of the dollar index, tumbled to its lowest level against the greenback since early April after European Central Bank policymaker Joerg Asmussen told Reuters Insider that forward guidance on interest rates extends beyond 12 months. He also said he would not rule out other potential policy action. Abandoning its traditional policy of never pre-committing on future rates, 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. In midday New York trade, the dollar index, which measures the greenback against a basket of six currencies, rose as high as 84.753 - a three-year peak. It last traded at 84.684, up 0.6 percent on the day. "The outlook for continued easy monetary policy from the ECB for over a year, contrasts with expectations for the Fed to begin removing policy accommodation, possibly as early as September," said Omer Esiner, chief market analyst at Commonwealth Foreign Exchange in Washington, D.C. The euro dropped to $1.2760, its lowest since early April. It last traded down 0.7 percent at $1.2778. The single currency, which began July above $1.30, had earlier found support after Greece secured aid that will prevent it from defaulting in August. Expectations the Fed, which releases minutes from its June monetary policy meeting on Wednesday, will scale back its $85 billion-a-month in asset purchases as early as September are encouraging investors to buy dollars. "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." Similarly, any modest decline in the dollar in the coming days "will provide a renewed buying opportunity as the overall picture is positive for the dollar," said Ian Stannard, head of European FX strategy at Morgan Stanley. He said Wednesday's FOMC minutes would be scrutinized for any hints to when Fed monetary stimulus could be reduced. Last week's U.S. employment report fueled expectations that the Federal Reserve could soon scale back its stimulus. In contrast, the European Central Bank and the Bank of England are widely seen as more likely to ease monetary policy. The Bank of Japan, meanwhile, is expected to continue with aggressive stimulus. The most recent Commodity Futures Trading Commission data showed long-dollar positioning building into the end of the second quarter, but still below the peak seen in May, suggesting further upside for the greenback. The value of net long positions in the dollar jumped to $22.37 billion in the week ended July 2 from $13.28 billion the previous week. The dollar also gained sharply against the British pound, after weaker-than-expected data highlighted how Britain's economy is lagging the strength seen in the United States. Sterling was weighed by 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. Sterling fell 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. The dollar also gained against the yen as the Bank of Japan is expected to maintain aggressive monetary stimulus when it meets to decide on policy later this week. The dollar rose 0.2 percent to 101.18 yen, according to Reuters data.