Inflation cooled annually, but the details are more worrying.

Inflation cooled very slightly on an annual basis for a seventh straight month in January, continuing a deceleration that has come as supply chains have healed and prices for goods have moderated, but the details of the report offered reasons for concern.

Consumer Price Index data released on Tuesday showed that price increases picked up briskly on a monthly basis. That was true across both key measures: the one that includes gas and groceries, and a “core” index that strips out those products because of their month-to-month volatility to get a better sense of the underlying inflation trend.

The price index was up 6.4 percent in January compared with a year earlier. That was a slight slowing from 6.5 percent in December, and down notably from a peak of about 9 percent last summer. But compared with the previous month, prices climbed 0.4 percent after stripping out groceries and fuel — a rapid pace of growth that matched the increase in December.

The overall report shows that while the Federal Reserve has been receiving positive news on inflation — price increases are no longer relentlessly accelerating, the way they did for much of 2021 and the first half of 2022 — it could be a long and bumpy road back to the 2 percent annual inflation gains that used to be normal.

“We’re certainly down from the peak of inflation pressures last year, but we’re lingering at an elevated rate,” said Laura Rosner-Warburton, senior economist at MacroPolicy Perspectives. “The road back to 2 percent is going to take some time.”

Pricier hotels, car insurance and vehicle repairs and a continued rapid increase in rental costs are among the factors that helped to keep inflation figures high in January. Goods, including used cars and clothing for women, dropped in price on a monthly basis, but even the slowdown in some physical products was less pronounced than it had been. Price increases for overall apparel accelerated, for instance.

The fresh data underline that price pressures remain stubborn and inflation may not fade quickly and smoothly, something Fed officials have repeatedly warned about.

“There has been an expectation that it will go away quickly and painlessly — and I don’t think that’s at all guaranteed,” Jerome H. Powell, the Fed chair, said at an event last week.

Central bankers have been waiting for the ongoing cool-down in price increases to become more broadly based. Much of the inflation slowdown in recent months has come from a moderation in price increases for goods and commodities. After stripping those out, services inflation — which includes health care, restaurant meals, pedicures and other non-goods purchases — has remained unusually rapid and has shown little sign of slowing down.

That trend continued in January, with services prices excluding energy continuing to increase rapidly, partly owing to the jump in rental and other housing costs. A measure that Mr. Powell watches closely, which tracks services after stripping out housing in addition to food and gas, eased slightly last month.

Rent inflation is expected to slow in the months ahead as a recent pullback in asking rents on newly leased apartments slowly shows up in official inflation data. But how much — and for how long — rent increases will fade is uncertain.

“It is a little bit unclear what the underlying momentum is in shelter,” said Sonia Meskin, head of U.S. macro at BNY Mellon Investment Management, explaining that strong job gains and solid wage growth could keep pressures on the market. “Shelter tends to correlate with a tight labor market.”

Officials at the Fed have been closely watching to see whether service price increases can decelerate, betting that it will probably be necessary to drive them lower in order to return inflation to the 2 percent that they aim for on average and over time. Central bankers define their inflation goal using a related but more delayed inflation measure.

Policymakers are worried that it could be challenging to wrestle inflation back to normal at a moment when the labor market is so strong, in part because companies may charge more as they pay more to compete for a limited pool of workers. Wages are a major cost of doing business for many service providers.

Employers added more than half a million jobs in January, an unexpectedly robust number, and gains in average hourly earnings and other pay trackers remain rapid, though they have begun to slow.

How strong inflation and the overall economy prove in the coming months will influence how high Fed policymakers ultimately lift interest rates and how long they keep them elevated. Central bankers have lifted their main policy rate from near-zero to more than 4.5 percent in less than a year, and have forecast that they will climb slightly above 5 percent.

“The base case for me is that it will take some time, and we’ll have to do more rate increases, and then we’ll have to look around and see whether we’ve done enough,” Mr. Powell said last week.

For now, mounting evidence suggests that inflation is not fading as quickly as economists had hoped even a month or two ago, said Jason Furman, an economist at Harvard University and a former Obama administration economic adviser.

“The inflation picture that had started to look better a month ago, it turns out that a lot of that was probably a false dawn,” Mr. Furman said. “The whole perspective we have on inflation is much worse.”