Inflation remained elevated in July as the economic recovery continued, but prices showed evidence of cooling amid pandemic-related supply problems and signs that the recent rise in coronavirus infections is starting to crimp some business activity.

Consumer prices rose 5.4% in July from a year earlier, the same pace as in June, the highest 12-month rate since 2008, the Labor Department reported Wednesday.

On a monthly basis, however, price pressures weakened. The department’s consumer-price index climbed a seasonally adjusted 0.5% in July from June, a significantly slower pace than its 0.9% increase in June from May, though well above the average 0.2% rate from 2000 to 2019.

The CPI measures what consumers pay for goods and services, including groceries, clothes, restaurant meals, recreation and vehicles.

The so-called core price index, which excludes the often volatile categories of food and energy, increased 4.3% from a year before, down from a 4.5% annual increase in June. Month to month, the core CPI rose 0.3%, also down sharply from the 0.8% average increase in the previous three months.