A measure of inflation closely watched by the Federal Reserve continued to cool on an annual basis in January, the latest sign that price increases are coming back under control even as the economy continues to chug along.

The Personal Consumption Expenditures price index climbed 2.4 percent last month compared with a year earlier. That was in line with what economists had forecast and down from the 2.6 percent December reading.

After stripping out food and fuel costs, which can move around from month to month, a “core” price index climbed 2.8 percent from January 2022. That followed a 2.9 percent December reading.

Still, the closely watched core measure climbed more quickly on a monthly basis: It picked up by 0.4 percent, quicker than a 0.1 percent December pace. That was the fastest pace of increase since January 2023, and it came as service prices continued to climb at a rapid clip.

Taken as a whole, the data provide further evidence that while inflation continues to come down, the path back to normal could remain at least somewhat bumpy.

Fed officials aim for 2 percent price increases, so today’s inflation rate remains elevated. Still, it is much lower than this measure’s roughly 7 percent peak in 2022. In their December economic projections, central bankers predicted that inflation would cool to 2.4 percent by the end of the year.

“They’re probably not going to get too worked up over just one print,” said Omair Sharif, founder at Inflation Insights, but he noted that policymakers were likely to pay attention to the firm monthly inflation reading. “This is obviously going in the wrong direction.”

Policymakers meet next on March 19-20, and the latest inflation data could factor in to how they are thinking about the economy. Policymakers are likely to take this report together with a more up-to-date inflation measure, the Consumer Price Index, which is set for release on March 12.

Officials have recently been able to dial back their campaign to slow the economy because price increases have been swiftly cooling.

Fed officials have already raised interest rates to a range of 5.25 to 5.5 percent, up sharply from near zero as recently as early 2022. But they skipped a final rate increase that they had previously predicted in 2023, and have signaled that they could cut interest rates several times this year.

Investors are now wondering how soon those rate cuts could come, and how quickly they will proceed. But Fed officials have been taking a wait-and-see approach, worried about declaring victory before inflation is firmly stamped out.

“While we’ve seen great progress toward achieving our goals, the journey is not yet over,” John C. Williams, the president of the powerful Federal Reserve Bank of New York, said in a speech this week. But he said that there were risks on both sides.

“Inflation may surprise on the upside, or consumer strength — a major driver of the robust growth we saw in 2023 — may fade more quickly than I anticipate,” he said.

Mr. Sharif pointed out that while there was a lot of “hoopla” in recent months about the fact that inflation had moved down sharply on a six-month basis, the latest report shores up the Fed’s reasons for caution. It shows that the number “is kind of going to opposite way now.”

It might be particularly relevant to policymakers that the monthly pickup is coming from service categories, and partly from purchases like health-care and hospitality. Those measures can be slow-moving and tie back to the strength of the economy, so the Fed watches them closely.

Thursday’s report also included a fresh reading on consumer spending, and suggested that consumers spent less in inflation-adjusted terms last month.

“We have expected consumers to reign in their spending this year after drawing down the pandemic-related savings,” Kathy Bostjancic, the Nationwide chief economist, wrote in a note following the report.

At the same time, a measure of personal income climbed more than expected, in part as social security payments were adjusted for the cost of living and as dividend income climbed. Such gains amid slowing price increases could give shoppers continued wherewithal to spend this year.