New-car prices edge up, while buying a used car gets cheaper.

The Consumer Price Index climbed 5 percent in the year through March, down from 6 percent in February. That marked the slowest pace since May 2021.

Still, the details of the report underlined that inflation retains concerning staying power under the surface: A so-called core index that aims to get a clearer sense of price trends by stripping out food and fuel costs, both of which can be volatile, picked up by 5.6 percent from a year earlier. That was up slightly from February’s 5.5 percent increase, and it marked the first acceleration in the yearly number since September.

The mixed signals in the fresh inflation data — which, taken as a whole, suggested that price increases are meaningfully moderating but the progress remains gradual — come at a challenging economic moment for the Federal Reserve. The central bank is the government’s main inflation fighter, and it has been trying to wrestle price increases back under control for slightly more than a year, raising interest rates to nearly 5 percent from near zero as recently as March 2022 to slow the economy and weigh down costs.

Officials are now assessing how their policy changes are working, and they are trying to gauge how much more they need to do to ensure that price increases come fully under control. Inflation has been slowing after peaking at about 9 percent last summer, but the process has been a slow one. It remains a long way back to the 2 percent inflation that was normal before the onset of the pandemic in 2020.

Uncertainty over how quickly and completely price increases will cool is being compounded by recent developments. A series of high-profile bank blowups last month could slow the economy, but it is unclear by how much. Some Fed officials are urging caution in light of the turmoil, even as others warn that the central bank should keep its foot on the economic brake and remain focused on its fight against rising prices.

The new data “solidifies the case for the Fed to do another hike in May, and to proceed cautiously from here,” said Blerina Uruci, chief U.S. economist at T. Rowe Price, later adding that “it will take time to bring inflation down.”

Fed officials target 2 percent inflation, which they define using a different index: the Personal Consumption Expenditures measure, which uses some data from the consumer price measure but is calculated differently and released a few weeks later. That measure has also been sharply elevated.

While Wednesday’s report showed an uptick in core inflation on an annual basis — one that economists had largely expected — Ms. Uruci said that it also offered some encouraging signs. The core inflation measure slowed slightly on a monthly basis, when the March figures were compared to those in February.

And a few important services prices, which the Fed is watching closely for a sense of whether price increases are poised to fade, cooled notably. Rent of primary residences picked up 0.5 percent compared to the prior month, down from 0.8 percent in the previous reading, for instance. Housing inflation broadly is expected to slow in 2023, and that appears to be starting to take hold.

“There are signs in the details to suggest we’re making some progress toward slowing inflation,” Ms. Uruci said. “It’s not where it needs to be, but it’s progress.”

But those hopeful signs do not mean that inflation will fade smoothly and rapidly. The slowdown in the overall index, for instance, may not last: A big chunk of the decline is owed to a drop in gas prices that may not be sustained.

And a few other indexes continued to show quick price increases, including new vehicles and hotel rooms.

As they try to bring inflation to heel, some central bankers have suggested that they may need to further raise interest rates.

The Fed’s latest estimates, released shortly after the collapse of Silicon Valley Bank and Signature Bank in March, suggested that officials could lift rates another quarter-point this year, to just above 5 percent. The central bank will announce its next policy decision on May 3.

On Tuesday, John C. Williams, the president of the Federal Reserve Bank of New York, said that the Fed had more work to do in bringing down price increases and suggested that the central bank’s March forecast for one more quarter-point rate move was still a “reasonable starting place.”

But Austan D. Goolsbee, the president of the Federal Reserve Bank of Chicago, suggested that recent bank failures could make it tougher for businesses and consumers to access credit, slowing the economy, stoking uncertainty and creating a “need to be cautious.”

“We should gather further data and be careful about raising rates too aggressively until we see how much work the headwinds are doing for us in getting down inflation,” Mr. Goolsbee said.

Higher interest rates have made it much more expensive to borrow money to buy a house or expand a business. That is slowing economic activity. As demand cools and the labor market softens, wage growth is also moderating.

That could help to pave the way for cooler inflation. When wages are climbing quickly, companies might charge more to try to cover their labor bills, and their customers are likely to be able to afford the steeper prices. But as households become more strapped for cash, it could become harder for businesses to raise prices without scaring away shoppers.