Inflation has slowed from its painful 2022 peak but remains uncomfortably rapid, data released Tuesday showed, and the forces pushing prices higher are proving stubborn in ways that could make it difficult to wrestle cost increases back to the Federal Reserve’s goal.

The Consumer Price Index climbed by 6.4% in January compared with a year earlier, faster than economists had forecast and only a slight slowdown from 6.5 percent in December. While the annual pace of increase has cooled from a peak of 9.1% in summer 2022, it remains more than three times as fast as was typical before the pandemic.

And prices continued to increase rapidly on a monthly basis as a broad array of goods and services, including apparel, groceries, hotel rooms and rent, became more expensive. That was true even after stripping out volatile food and fuel costs.

Taken as a whole, the data underscored that while the Federal Reserve has been receiving positive news that inflation is no longer accelerating relentlessly, it could be a long and bumpy road back to the 2% annual price gains that used to be normal. Prices for everyday purchases are still climbing at a pace that risks chipping away at economic security for many households.