* Speculation of Fed easing weighs broadly on dollar * Moody's warning on U.S. debt hurts dollar * Euro at 4-month high, Canadian dollar at 1-year peak By Julie Haviv NEW YORK, Sept 11 (Reuters) - The U.S. dollar fell against most major currencies on Tuesday on expectations the Federal Reserve will soon unveil new economic stimulus measures and losses accelerated after Moody's Investors Service raised fears about a credit rating downgrade of the United States. Moody's said the U.S. could lose its triple-A debt rating if next year's government budget talks do not result in a lower debt to GDP ratio. The euro also hit a four-month high on expectations a German constitutional court will approve the euro zone bailout fund, or ESM, fueling further optimism about a resolution of the region's debt crisis following the European Central Bank's decision last week to buy bonds from highly indebted countries. "That just removes the uncertainty about the bailout fund which is euro-positive and the consensus now is that the German court will back the fund without incident," said Brian Kim, currency strategist, at RBS Securities in Stamford, Connecticut. The euro last traded at $1.2864, up 0.8 percent on the day, after earlier hitting a peak of $1.2871, its highest since May 14 after it rose above its 200-day moving average around $1.2834. The euro, which has recovered strongly since hitting a two-year low of $1.2042 in late July, still faces the risk Germany's constitutional court could still surprise investors by rejecting the European Stability Mechanism, Europe's new bailout fund, in a ruling on Wednesday. Such a decision would threaten European Central Bank plans to lower the borrowing costs of Spain and Italy under a program announced late last week which gave the euro a lift. The German court said it would not postpone Wednesday's long-awaited decision despite a new challenge by a eurosceptic lawmaker. Market participants will also be watchful of news from the Netherlands which holds an election on Wednesday. Analysts said sentiment toward the euro was broadly positive but the currency was vulnerable to developments in Spain, which is expected to ask for a bailout, and in Greece, whose foreign lenders rejected parts of a government austerity package. "Spain and Italy are huge problems that are far from solved, and if the worst comes and the (bailout funds) are tapped and the ECB starts purchasing 'unlimited' quantities, ... the euro will devalue, similar to the dollar when the Fed initially started its quantitative easing program," said Brad Bechtel, managing director at Faros Trading in Stamford, Connecticut. WEAK DOLLAR Weak U.S. jobs data last week raised expectations the Fed will launch another asset purchase program. That would weigh on the dollar against higher-yielding currencies. In a Reuters poll taken after Friday's weaker-than-expected payrolls report, economists saw a 60 percent chance of the Fed embarking on quantitative easing this week compared with 45 percent in a late August poll. The greenback last traded at 77.74 yen, its lowest in more than three months. Analysts said the Japanese authorities were likely to step up threats to intervene in the currency market and the Bank of Japan could ease policy further when it meets next week to offset any impact from possible easing by the Fed. The growth-linked Canadian dollar rose to a one-year high against the U.S. dollar, buoyed in part by the Bank of Canada's tightening bias. The U.S. dollar was last down 0.6 percent at C$0.9718, according to Reuters data.