NEW YORK — New York Federal Reserve President John Williams on Tuesday cautioned that interest rate increases will take a while to work their way through the economy before inflation returns to an acceptable level.

The central bank official gave no forecast for where he sees policy headed but said he doesn’t expect inflation to return to the Fed’s 2% goal until the next two years. Should inflation not come down, he said the Fed always has the option to raise rates.

He added that unemployment is likely to rise to a 4%-4.5% range, from its current 54-year low of 3.4%.

“Because of the lag between policy actions and their effects, it will take time for the [Federal Open Market Committee’s] actions to restore balance to the economy and return inflation to our 2% target,” Williams said in prepared remarks at the Economic Club of New York.

Williams spoke six days after the FOMC voted to raise its benchmark rate another quarter percentage point to a target range of 5%-5.25%. In its post-meeting statement, the committee hinted it could pause rate hikes, though it said officials will be taking a variety of factors into account when determining how to proceed.

The committee removed a key phrase from the statement that had indicated additional rate hikes would be appropriate. Williams said that decision is now a matter of what the incoming data says.

“First of all, we haven’t said we’re done raising rates,” Williams told CNBC’s Sara Eisen during a Q&A session after his speech. “We’re going to make sure we’re going to achieve our goals and we’re going to assess what’s happening in our economy and make the decision based on that data.”

“I do not see in my baseline forecast, any reason to cut interest rates this year,” he said, adding that additional rate hikes would be possible if the data don’t cooperate.

The current problems in the banking industry and their impact will factor into Williams’ policy outlook, he said.

“I will be particularly focused on assessing the evolution of credit conditions and their effects on the outlook for growth, employment and inflation,” Williams said.

Some positive signs Williams cited include moderation in longer-term inflation expectations and a cooling in demand for labor that has heated the jobs market and put upward pressure on wages, which nonetheless have failed to keep up with cost-of-living increases.

He also said clogged labor chains, which have been a major inflation contributor, have “improved considerably” over time.