New York Federal Reserve President William Dudley said on Monday it is too early to talk about curtailing the central bank's long-term security purchases while the economic recovery is fragile.

As financial conditions improve, which seems to be the trajectory, it's a legitimate point to consider what you want to do in terms of your purchase programs, Dudley told CNBC in an interview.

My own personal view is I think it's a little premature to be so confident that you want to pull all these things back right now because the economy still isn't growing very fast and we do have a very high unemployment rate.

Dudley's comments show a divergence of views on the Fed's interest-rate setting Federal Open Market Committee. Richmond Fed President Jeffrey Lacker said last week the Fed should consider foregoing the full extent of its long-term securities- buying pledge, which includes the plan to purchase $1.45 trillion of mortgage agency debt by the end of the year.

The Fed cut rates to zero in December and has pumped hundreds of billions into the financial system to spur economic growth in the worst recession in 70 years. With signs of recovery in housing and factory activity, the Fed has said the downturn appears to be leveling out, but with the caveat that any recovery is likely to be sluggish with unemployment painfully high for a while.

Dudley said on Monday he is confident the U.S. central bank can withdraw its massive economic stimulus measures without allowing dangerous inflation to take hold.

We have tools to manage our balance sheet so that we're not going to have an inflation outcome, bad inflation outcome, Dudley told CNBC in an interview.

(Reporting by Mark Felsenthal; editing by Stephen Nisbet)