By Jonathan Spicer (Reuters) - Once the Federal Reserve reduces its bond-buying program, it could then wait "a number of years" before it raises interest rates, an influential official at the U.S. central bank said on Friday. The two things "are very loosely connected," said New York Fed President William Dudley. "The amount of time that can pass between the decision to begin to taper and actually raising short-term interest rates could easily be a number of years." Dudley, a close ally of Fed Chairman Ben Bernanke, was speaking a week after the Fed stunned financial markets with its decision not to reduce its bond-buying program from the current $85-billion monthly pace, setting off a stock rally around the world. Over the summer, investors had driven up longer-term interest rates in anticipation of the first cut to the quantitative easing program, causing concern among Fed officials who have sought to convince the world they are nowhere near ready to tighten policy. The central bank has repeatedly promised to keep its key rate near zero at least until the jobless rate falls to 6.5 percent, as long as inflation remains contained. "These are two separate issues: adding accommodation at a slower rate and ultimately not adding any more accommodation, versus actually tightening monetary policy," Dudley, a permanent voting member of the Fed policy committee, told students at Syracuse University. "People should not assume that just when we get to the point where we actually start to reduce the pace of asset purchases that we're actually about to tighten monetary policy." In his prepared speech, Dudley repeated a strong defense of keeping up QE at its current pace, and said the economic recovery still needs support. He pointed to conflicting information on the U.S. labor market, which was badly bruised by the Great Recession but has improved in recent years, with unemployment now down to 7.3 percent from a 10-percent peak in 2009. "Job loss rates have fallen, but hiring rates remain depressed at low levels. Taken together, the labor market still cannot be regarded as healthy," Dudley said. "Numerous indicators, including the behavior of labor compensation, are all consistent with the view that there remains a great deal of slack in labor markets," he said. As for currently soft inflation readings, Dudley said he expects it to "firm further in the months ahead" and move toward the Fed's 2-percent goal. Still, he said, the Fed "recognizes that inflation persistently below 2 percent could pose risks to economic performance." He also repeated a warning about politicians undercutting the U.S. recovery. "In coming weeks, Congress will be considering how to fund the government for the next fiscal year and will also be debating what to do about the debt limit," Dudley said. "This creates uncertainty about the fiscal outlook and may exert a restraining influence on household and business spending." (Reporting by Jonathan Spicer; Editing by Chizu Nomiyama)