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.

(Reporting by Mark Felsenthal; Editing by Ron Askew)