* Dollar falls to 7-month low versus yen * Euro stays near 4-month high against dollar * Dollar could extend falls if Fed opts for more stimulus * SNB keeps Swiss franc cap at 1.20 per euro By Jessica Mortimer LONDON, Sept 13 (Reuters) - The dollar fell on Thursday, hitting a seven-month low against the yen and holding near a four-month low versus the euro on signs the Federal Reserve may announce a third bout of monetary stimulus. Many in the market expect the Fed to unveil a new 'QE3' asset purchase programme when it gives its policy decision at 1630 GMT. This would likely cause the dollar to extend losses. The dollar fell to 77.58 yen, its lowest since mid-February. Further falls would put markets on alert for possible intervention in Tokyo to stem the rise in the Japanese currency, traders said. The euro was up 0.15 percent at $1.2919, near a four-month high of $1.2937 reached on Wednesday. It remained firm after Germany's Constitutional Court on Wednesday cleared ratification of the euro zone's permanent rescue fund, paving the way for the European Central Bank to buy bonds of struggling countries in the region. "Although the market broadly expects more easing from the Fed, the euro should pop up (if the Fed announces more easing). It might get almost to $1.30 and next week should consolidate around that level," said Gavin Friend, currency strategist at National Australia Bank. The euro has been buoyant since the ECB announced plans last week to buy potentially unlimited amounts of government bonds issued by indebted states like Spain and Italy to reduce their borrowing costs. "We are talking about a significant reduction in the tail risks surrounding the euro zone," Friend said, adding he expected the euro to trade in a higher range of between $1.26 and $1.31. If the Fed fails to deliver the stimulus anticipated, he predicted the euro's falls would be limited to around $1.2850. But traders cited chart resistance for the euro at the 233-day moving average at $1.2938 while a reportedly large options expiry at $1.2900 later in the day could influence price action and keep the euro trading close to that level. The currency has risen more than 7 percent from July's two-year low of $1.2042, buoyed after an ECB pledge to do whatever it takes to preserve the currency. "If the Fed avoids major easing steps, the euro could fall. Still, considering that the euro's rally has been driven by short-covering rather than build-up of new positions, downside for the euro may be limited," said Koichi Takamatsu, head of forex at Nomura Securities in Tokyo. The Swiss franc was slightly weaker, having briefly risen earlier on relief the Swiss National Bank did not weaken the franc cap from its current level of 1.20 per euro. The SNB said the Swiss franc was "still high" and threatened to take further steps if necessary. The common currency was last up 0.1 percent at 1.2102 francs . ALL EYES ON FED Mounting expectations the Fed might print more dollars, thereby cheapening their value, pushed the dollar index down 0.1 percent to 79.640, keeping it near a four-month low of 79.522 on Wednesday. Many Fed watchers believe any new asset purchase programme would be open-ended, unlike the past two cycles of quantitative easing. That would allow the central bank to review the size of its purchases on a frequent basis and adjust the programme as economic circumstances warranted. "The market has not 100 percent priced in QE3 yet," said Masafumi Yamamoto, chief FX strategist at Barclays, noting that whether the monthly purchase size was larger than the previous QE round's $75 billion would be important, regardless of whether the new programme was open-ended or not. Also helping the euro was the result of elections in the Netherlands, where pro-European parties crushed radical fringe groupings, dispelling concerns that eurosceptics could gain a power base in one of the euro zone's core states. The euro dipped against the yen, trading at 100.21 yen but staying not far from Wednesday's high of 100.64 yen. Against the pound, it stood at 80.13 pence , having hit a 10-week high of 80.28 on Wednesday.