SYRACUSE, N.Y./GRAND RAPIDS, Mich. (Reuters) - A debate within the Federal Reserve over the outlook for U.S. inflation burst into public view just days after a rate-setting meeting in Washington, with one central banker saying inflation weakness is fading and another suggesting he’s nervous it won’t.

FILE PHOTO: A police officer keeps watch in front of the U.S. Federal Reserve building in Washington, DC, U.S. on October 12, 2016. REUTERS/Kevin Lamarque/File Photo

Both New York Federal Reserve Bank President William Dudley and Chicago Fed President Charles Evans said they believe the U.S. economy’s fundamentals are sound, and both said they support gradual rate hikes ahead.

But while Dudley reinforced Fed Chair Janet Yellen’s confident tone at the close of last week’s meeting that inflation is set to rise back to the Fed’s 2-percent target, Evans sounded much less certain.

“It’s really going to come down to the inflation situation -- it might take longer to sort out than some people think,” Evans said told reporters after a speech titled “the puzzle of low inflation” in Grand Rapids, Mich. “I’m a little nervous that some of the recent weakness might be a little more structural.”

Evans’ view appears to be in the minority at the Fed, where decisions on the appropriate level of interest rates are made every six weeks or so. The Fed has raised rates twice this year, and last week, though it held them steady, signaled it will likely raise them one more time this year and three times next.

Dudley cited the soft dollar and strong overseas growth among the reasons he expects slightly above-average U.S. economic activity and a long-sought rise in wages.

“With a firmer import price trend and the fading of effects from a number of temporary, idiosyncratic factors, I expect inflation will rise and stabilize around the (Fed’s) 2 percent objective over the medium term,” he told students and professors at Onondaga Community College.

“In response, the Federal Reserve will likely continue to remove monetary policy accommodation gradually,” added Dudley, a close ally of Yellen and a permanent voter on the Fed’s monetary policy committee.

Evans for his part appears less anxious to tighten policy in the face of price readings that have sagged since February, despite strong jobs growth.

He said that while he is open-minded about the next several meetings, “I’m looking for evidence that inflation will be moving up with momentum,” and it may take more than a couple of months for such a trend to show up in the data.

Futures traders give a December rate hike about a 72-percent probability, according to Reuters data.

Both policymakers nodded to the three devastating hurricanes that have struck parts of the U.S. south and the Caribbean, noting their effects will likely make it more difficult to interpret economic data in coming months.