* New bout of Fed easing lifts sterling
* Pound hits 4-month high vs dollar, more gains possible
* But falls to 3-month low versus buoyant euro
LONDON, Sept 14 (Reuters) - Sterling rose to a four-month high against the dollar on Friday after the Federal Reserve embarked on a fresh round of monetary easing to support economic growth, but it dropped sharply against a buoyant euro.
Equities and perceived riskier currencies, including the pound, gained after the Fed said it would pump $40 billion into the world's biggest economy each month until it saw a sustained upturn in a weak jobs market.
The pound rose more than half a percent to $1.6251, its strongest since late April. It was last at $1.6226.
Traders and analysts saw the potential for further gains due to the Fed's new bout of quantitative easing, which increases the supply of a currency and typically cheapens it, potentially taking it towards this year's high of $1.6304.
However, it hit a three-month low against the euro, which continued to outperform after the European Central Bank last week announced a bold plan to tackle the euro zone debt crisis, improving sentiment towards the region's assets.
"Sterling has vaulted sharply higher on the back of the Fed," said Neil Mellor, currency strategist at Bank of New York Mellon.
"The euro has gone up more so than sterling against the dollar and continues to look fairly bullish. Obviously the greater sense of stability in the euro zone is part of that."
The euro jumped 0.8 percent to 81.14 pence, its highest level since June 15.
More gains could take the euro towards its 200-day moving average of 81.48 pence and the mid-June peak of 81.63 pence as investors cut previous short positions when they were fleeing the euro into perceived safer alternatives, including sterling.
The single currency has risen strongly since Germany's Constitutional Court on Wednesday gave the green light to the euro zone's new rescue fund, paving the way for the ECB to implement its plan to lower borrowing costs for struggling countries.
However, the pound could also be lifted by recent data suggesting Britain could be set to exit recession and may outperform the euro zone.
"Enthusiasm for the euro could wear off as the ECB plan is only buying time ... Eighty pence (in euro/sterling) does feel about fair value at the moment and it is likely to continue to fluctuate around that level," said Alex Lawson, senior dealer at Moneycorp.
Sterling's falls against the euro pushed its trade-weighted index to 83.8, matching a low hit in late August. A move below this level would mark its weakest in a month.
MORE GAINS SEEN VERSUS DOLLAR
The Fed's third round of quantitative easing was perceived as particularly dovish because the central bank kept open the amount of assets it could purchase in order to support the economy.
"Sterling has more upside against the dollar after the Fed announced (potentially) unlimited amounts of QE ... It should be in for a prolonged period above $1.60," Moneycorp's Lawson said.
At the same time, better UK data has lessened concerns about the outlook for the economy and the prospect of more quantitative easing from the Bank of England.
The UK economy is already tipped to post some growth between July and September, with a Reuters poll on Wednesday pointing to 0.6 percent expansion, after data showed in July industrial output grew at its fastest pace in 25 years.
Figures on Friday showed UK construction activity grew 2.2 percent in July and fell less sharply than previously thought in the second quarter.