New York Fed President William Dudley said in a speech on Friday that the Fed's further interest rate hikes will be gradual and depend on the incoming economic data.

"Looking ahead, I'll talk about what comes next. No surprises here-it depends on the data. As noted in the December FOMC statement, we expect that the normalization of monetary policy will be quite gradual," he said.

Dudley expressed concerns about low inflation.

"With respect to the risks to the inflation outlook, the most concerning is the possibility that inflation expectations become unanchored to the downside. This would be problematic were it to occur because inflation expectations are an important driver of actual inflation," he noted.

"I expect the increase in resource utilization will be sufficient to push both inflation and inflation expectations higher over time. That said, should the economy unexpectedly weaken, then this fall in inflation expectations would become more concerning," New York Fed president added.