Richmond Federal Reserve President Thomas Barkin Monday said he is comfortable with the U.S. central bank moving to a data-dependent approach on whether to raise interest rates from here, but he is not yet convinced inflation is on a steady path downward.

Barkin, in an interview with Reuters, said he also is withholding making a decision on whether to raise rates at the Fed's June 13-14 policy meeting, given there is more economic data still to come and uncertainty around bank credit and the U.S. debt ceiling.