NEW YORK (Reuters) - The Federal Reserve would probably not be able to cut interest rates as aggressively as the last time around if it were faced with a U.S. recession in the next few years, New York Fed President William Dudley said on Monday.

Beginning in 2007, the U.S. central bank slashed rates by 5.25 percent as the financial crisis took hold. With rates having since remained near zero, Dudley said the Fed now has less policy room to respond and thus may be cautious about raising rates.

"If another recession were to happen in the next few years, it is likely that the FOMC would be unable to respond with a cut of such magnitude," Dudley, speaking at a private conference at the New York Fed, said of the policy-making Federal Open Market Committee.

"A risk management approach to monetary policy would suggest that the more concerned one is with the effectiveness of these policies at the zero lower bound, the more cautious one would be in the process of removing accommodation," he added in prepared remarks.

Dudley is a permanent voter on Fed policy and close ally of Fed Chair Janet Yellen.

(Reporting by Jonathan Spicer; Editing by Chizu Nomiyama)