The Federal Reserve’s preferred inflation measure climbed more slowly than economists had expected in the year through May after stripping out food and fuel prices — an encouraging sign that price increases are gradually moderating.

Although inflation has been cooling notably on an overall basis in recent months, Fed officials have been closely tracking the “core” inflation measure that cuts out grocery and gas costs, which they think offers a better signal of how price increases might shape up in the months and years to come. It has been stuck at an elevated level and slowing down only gradually, a source of concern for policymakers who have spent more than a year raising interest rates in a bid to tame price increases.

The May data broke with that trend, at least a little. Prices climbed 4.6 percent over the past year, excluding food and fuel. That compared with 4.7 percent in the previous month, which economists had expected would repeat itself. Core inflation is down from a 5.4 percent peak, but it remains well above the Fed’s 2 percent inflation goal.

Progress in wrestling overall inflation has been swifter. The Personal Consumption Expenditures index measure that includes food and gas climbed 3.8 percent in the year through May, in line with economists’ forecasts. That measure peaked at about 7 percent last summer.

More moderate overall inflation is taking some pressure off consumers: Cheaper tanks of gas and less rapid price increases in the grocery aisle are helping paychecks to go further. But for officials at the Fed, signs that inflation remains stubborn under the surface have been a reason to worry. Officials believe that they need to wrestle core price increases lower to make sure that the economy’s future is one of modest and steady price increases.

To do that, Fed policymakers have been raising interest rates. Making it more expensive to get a home loan or expand a business restricts the economy’s momentum. By slowing growth and cooling demand, the moves are meant to make it harder for corporations to increase their prices without losing customers.

Policymakers skipped a rate increase at their June meeting after 10 straight moves, but they have signaled that they expect to lift rates beyond their current level of just above 5 percent — perhaps to 5.5 percent by the end of the year. Investors have been betting on only one more move this year, but they increasingly see two rate moves as a possibility.

Jerome H. Powell, the Fed chair, emphasized this week at an event in Madrid that the outlook for how much more rates might move this year is uncertain.

“We’ve all seen inflation be, over and over again, shown to be more persistent and stronger than expected,” Mr. Powell said. “At some point that may change. And I think we have to be ready to follow the data and be a little patient as we let this unfold.”

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