Inflation cooled less than expected in January and showed worrying staying power after volatile food and fuel costs were stripped out — a reminder that bringing price increases under control remains a fraught, bumpy process.

The overall Consumer Price Index was up 3.1 percent from a year earlier, which was down from 3.4 percent in December but more than the 2.9 percent that economists had forecast. That figure is down from the latest peak of 9.1 percent in the summer of 2022.

But after stripping out food and fuel, which bounce around in price from month to month, “core” prices held roughly steady on an annual basis, climbing 3.9 percent from a year earlier. The measure jumped by the most in eight months on a monthly basis.

American consumers, the White House and Federal Reserve officials had welcomed a recent moderation in inflation. Central bankers in particular are likely to take the fresh report as a reminder that they need to remain cautious. Policymakers have been careful to avoid declaring victory over inflation, insisting that they needed more evidence that it was coming down sustainably.

Investors sharply pared back chances for an imminent Fed rate cut, betting that central bankers will not lower interest rates at their next meeting in March and sharply dialing back the odds that the Fed will do so even at its meeting in May — a sign that they think the fresh inflation figures will keep officials wary. Stock markets tumbled as traders revised their forecasts for Fed actions.

Fed policymakers have raised interest rates to about 5.3 percent, up from near zero in early 2022, in a bid to cool consumer and business demand and force companies to stop raising prices so quickly. Because inflation has been coming down notably in recent months, they have paused their rate increases and are contemplating when and how much to lower borrowing costs.

But they want to avoid cutting rates before inflation is fully snuffed out, because they worry that doing so could allow rapid price increases to become a more permanent feature of the American economy.

“They were right to be patient, because this is the kind of number that is going to cast doubt on whether there really is a lot of deceleration in store for inflation,” said Omair Sharif, founder of Inflation Insights. “This is definitely a spooky number.”

Slower inflation over recent months had also been a welcome development for President Biden. Surging living expenses have eaten away at household budgets, weighing on voter confidence even though the job market is strong and wages are climbing at a brisk pace. As price increases have begun to ease, people have started to report sunnier economic outlooks.

But the fresh inflation report could cast doubt on whether the cool-down over the previous six months will continue. The Fed has been paying close attention to whether that trend would persist.

“Is it sending us a true signal that we are, in fact, on a path — a sustainable path — down to 2 percent inflation?” Jerome H. Powell, the Fed chair, said during his Jan. 31 news conference. “That’s the question.”

The Fed aims for 2 percent inflation on average using a separate but related measure, the Personal Consumption Expenditures index. That gauge is set for release on Feb. 29.

Part of the problem with Tuesday’s report, from the Fed’s perspective, is that the pickup in the core inflation index came from services: Prices for airfares, hotel rooms, haircuts and financial help all climbed in January. Service inflation tends to be driven by slow-moving forces like wage growth, and it can be very stubborn.

And while the hotter-than-expected inflation figures were just one month of data, they came alongside other evidence that the economy was growing more quickly than expected. Hiring picked up in January, wage growth was solid, and consumers continue to spend.

Some analysts have suggested that in an economy this hot, wrestling inflation the rest of the way to normal will prove more difficult than the initial cool-down. In other words, the “last mile” on inflation might be the toughest one. Tuesday’s report could give that argument more heft.

“It is too early to declare victory over inflation,” said Torsten Slok, chief economist at Apollo Global Management. He noted that key economic measures like hiring picked back up after the Fed hinted late last year that it was done with rate increases — evidence of the potential risks of backing off too early.

“The last mile will be harder,” Mr. Slok said.

So far, bringing inflation down has been less painful than economists had expected. Many had predicted that it would take a substantial cooling in the economy — and a jump in unemployment — to lower price increases. Instead, inflation has fallen gently even with a strong job market.

The cool-down came partly as supply chains healed. Prices for goods started jumping in 2021 as shipping route and factory disruptions tied to the pandemic left semiconductors, automobiles and furniture in short supply. Those problems have been clearing, allowing goods prices to calm or even drop. Used car prices fell sharply in January, for instance.

But even as goods inflation fell, the question remained: Could service price increases moderate without a broader economic slowdown?

For a while, that seemed to be happening, but the trend stalled out in January. Economists are likely to watch the next several months of data to determine whether that is a blip — or the start of a new and concerning trend.

One services category is likely to remain in especially close focus: housing. Rents have been climbing more slowly in recent months, and many analysts have been expecting that trend to continue as cheaper new leases feed into official inflation figures. Housing makes up such a big chunk of American spending that the expected cooling would help to lower overall inflation.

But January’s report offered reasons for caution. A measure that estimates how much it would cost to rent a house that someone owns — called owner’s equivalent rent — picked up on a monthly basis.

The acceleration “looks at odds with other surveys of rent data that we monitor,” said Blerina Uruci, chief U.S. economist at T. Rowe Price.

On the whole, she said, the report underscores that the Fed will need to remain cautious.

“The main takeaway is that what Powell said during the January press conference was the right strategy,” Ms. Uruci said. “They really need to make sure that inflationary pressures will not re-accelerate before they can cut interest rates.”