* Fed will continue to do everything within power -Dudley * Depending on conditions, could do more on housing * QE3 one possible option, Dudley says * Dudley: Inflation rate should fall late this year, next * Fisher: Would not support more mortgage-backed buying By Jonathan Spicer NEW YORK, Oct 24 (Reuters) - The weak housing sector continues to pose a strong headwind to the U.S. economic recovery, and the Federal Reserve could potentially do more to drive down mortgage rates to support the sector, an influential Federal Reserve official said on Monday. William Dudley, president of the New York Federal Reserve Bank, said another round of quantitative easing, or QE3, is one possible option the U.S. central bank has to boost the slow recovery. "I don't think the Fed has run out of bullets," he said. Dudley also warned about "spillover" effects from Europe's debt crisis, which he predicted would be solved. But his comments on housing in particular could raise the stakes in the debate over what, if anything, the U.S. central bank should do next. It was the third time in a week that a Fed policymaker highlighted the possibility that the central bank could do more to support the housing market, a persistent drag on the recovery. A glut of foreclosed homes on the market and tight credit have contributed to a sector virtually stuck in the mud and unable to gain traction. "Breaking this vicious cycle is one of the most pressing issues facing policymakers," Dudley said in a speech at Fordham University's Gabelli School of Business. "Clearly we've indicated our interest in supporting the housing market in keeping mortgage rate spreads, and spreads between mortgage rates and Treasury yields, from getting too elevated," he said. "Depending on how the world evolves, we potentially could move to do more in that direction." The government on Monday, in a move to help homeowners whose homes are worth less than they owe, eased the terms of a refinancing program that helps so-called underwater borrowers who have been on time with payments but are unable to refinance.The overhaul, however, would help only a fraction of the 11 million underwater borrowers. Dudley, who as head of the New York Fed has a permanent voting seat on the Fed's policy-setting committee, said the central bank will continue to do everything in its power to help the economic recovery. Dudley's comments come on the heels of remarks by Fed Governor Daniel Tarullo last week that there was "ample room" for policymakers to do more to spur growth and that more mortgage-related securities purchases should be on the table. QE3? Faced with the worst recession in decades, the Fed in late 2008 cut rates to near zero. It followed with the purchase of $2.3 trillion in debt in two consecutive rounds of extraordinary measures known as quantitative easing -- more familiarly dubbed QE1 and QE2 -- to spur a recovery. The purchase of mortgage securities was a controversial part of QE1 in 2009; some officials criticized it for propping up a specific sector of the economy. Dudley, who gave back-to-back speeches in the New York City borough of the Bronx, called the housing market "a serious impediment" to a stronger recovery, which this year has been plagued by "quite disappointing" growth in gross domestic product. The rebound has been weak and is now threatened by Europe's debt crisis, casting doubt on the central bank's strategy and effectiveness but also raising some expectations for more asset purchases. "The Fed is doing -- and will continue to do -- everything within its power to promote jobs and price stability," said Dudley. Later, addressing the Bronx Chamber of Commerce, he said "quantitative easing round three" was a possible option. "Without robust growth, the economy is more vulnerable to negative shocks, which unfortunately seem to keep coming," Dudley said. "It is like riding a bicycle -- at a slow speed, the bicycle wobbles and the risk of falling rises." Another Fed regional president, Richard Fisher of the Dallas Fed, said he would be reluctant to endorse more aid to the housing sector. "There are other initiatives that the fiscal and other authorities can take that would possibly pick housing up off the floor, but I think it is going to be a very long-term process," said Fisher, who spoke in Toronto. "I think we have to be careful not to get into fiscal initiatives at the central bank." INFLATION VS UNEMPLOYMENT Europe, meanwhile, threatens to drag the world into another recession as policymakers there wrangle over a possible Greek default and its impact on the European banking system. Dudley, citing the effect on stock markets and on bank lending, said: "To date, these effects have been much more acute in Europe than in the United States, but there are spillovers to our nation, and we need to monitor them carefully." However, Dudley said he sees the inflation rate, which has been higher than the Fed's preferred level of 2 percent, falling, barring more energy price jumps. "I believe that underlying fundamentals will help to subdue inflation over the next few quarters," he said. Fisher, whose dissenting votes on recent Fed easing put him on the opposite end of the policy spectrum from Dudley, agreed. "Inflation is not the problem in the United States right now," he said, adding that high unemployment is the biggest problem facing the U.S. economy. But Fisher did not advocate more action by the Fed. He said adding any more heft to the Fed's $2.8 trillion balance sheet would be of "questionable efficacy." Last month, the Fed announced a plan, known as Operation Twist, to replace $400 billion of short-term securities in its portfolio with longer-term debt in order to lower longer-term rates and stimulate the economy. Brian Sack, head of the New York Fed's markets group, told primary dealers in New York that the effect of Operation Twist is about equal in size to that of the Fed's second round of asset purchases. To date, he said, mortgage-backed securities purchases have gone smoothly with market liquidity "quite good."