* Euro seen extending rally to $1.35-1.36 * Yen falls on anxiety about intervention By Gertrude Chavez-Dreyfuss NEW YORK, Sept 14 (Reuters) - The dollar fell against most currencies on Friday, hitting a four-month low versus the euro, a day after the Federal Reserve announced a fresh round of monetary stimulus to boost a still lackluster U.S. economy. Despite the move away from the safe-haven dollar, the yen fell broadly on speculation Japanese authorities could intervene to cap its recent gains against the dollar. Expectations that the Bank of Japan could ease policy next week in response to the Fed's action will also likely undermine the yen, some traders said. The dollar rose 0.9 percent against the yen to 78.15 yen . Commodity currencies including the Australian and Canadian dollars also rallied against the greenback, pushing the dollar index to 78.729, its lowest level in more than four months. Some market players said the Fed's announcement on Thursday that it will pump $40 billion a month into the U.S. economy until the jobs market shows a sustained upturn, along with the European Central Bank's plan agreed last week to lower peripheral euro zone borrowing costs, could see an the euro extend its rally toward $1.35 in the near term. "Recent moves by both the Fed and the ECB to bolster growth have helped usher in a wave of risk-taking which has seen demand for lower-yielding, safer investments such as the dollar evaporate," said Joe Manimbo, senior market analyst at Western Union Business Solutions in Washington. The euro hit a peak of $1.3120 and was last at $1.3099, up 0.8 percent on the day, as a drop in peripheral bond yields prompted investors to buy the currency. The euro rose to an eight-month high against the Swiss franc of 1.2178 francs on trading platform EBS and hit a four-month high against the yen of 102.37 yen. The dollar fell to 0.9265 Swiss francs, its lowest level since mid-May. The Australian dollar hit a one-month high of US$1.0605 as riskier assets rallied. Risk-taking was also helped by better-than-expected U.S. retail sales last month, which rose 0.9 percent, the largest gain since February.