WASHINGTON — Annual inflation in the United States cooled last month yet remained elevated in the latest sign that the pandemic-fueled price surge is gradually and fitfully coming under control. Tuesday’s report from the Labor Department showed that the consumer price index rose 0.3% from December to January, up from a 0.2% increase the previous month. Compared with a year ago, prices are up 3.1%. That is less than the 3.4% figure in December and far below the 9.1% inflation peak in mid-2022. The latest reading is well above the Federal Reserve’s 2% target at a time when public frustration with inflation has become a pivotal issue in President Joe Biden’s bid for re-election. Excluding the volatile food and energy categories, so-called core prices climbed 0.4% last month, up from 0.3% in December and 3.9% over the past 12 months. Core inflation is watched especially closely because it typically provides a better read of where inflation is likely headed. The annual figure is the same as it was in December. Biden administration officials note that inflation has plummeted since pandemic-related supply disruptions and significant government aid sent it soaring three years ago. And a raft of forward-looking data suggests that inflation will continue to cool. Still, even as it nears the Fed’s target level, many Americans remain exasperated that average prices are still about 19% higher than they were when Biden took office. The mixed data released Tuesday could reinforce the caution of Fed officials, who have said they’re pleased with the progress in sharply reducing inflation but want to see further evidence before feeling confident that it’s sustainably headed back to their 2% target. Most economists think the central bank will want to wait until May or June to begin cutting its benchmark rate from its 22-year-high of roughly 5.4. The Fed raised its key rate 11 times from March 2022 to July of last year in a concerted drive to defeat high inflation. The result has been much higher borrowing rates for businesses and consumers, including for mortgages and auto loans. Rate cuts, whenever they happen, would eventually lead to lower borrowing costs for many categories of loans. In the final three months of last year, the economy grew at an unexpectedly rapid 3.3% annual rate. There are signs that growth remains healthy so far in 2024. Businesses engaged in a burst of hiring last month. Surveys of manufacturing companies found that new orders rose in January. And services companies reported an uptick in sales.