WASHINGTON — America’s employers posted fewer job openings in July than they had the previous month, a sign that hiring could cool in the coming months.

The Labor Department reported today that there were 7.7 million open jobs in July, down from 7.9 million in June. The pace of hiring picked up, though, from June to July.

Today’s figures indicate that fewer companies are seeking to add workers despite recent data showing that consumer spending is still growing. Last week, the government estimated that the economy expanded at a healthy 3% annual rate in the April-June quarter.

The number of job openings has been trending gradually down over the past year. Yet there are still roughly 1.1 job openings for every unemployed person, today’s report showed. That reflects the economy’s continuing need for workers and marks a reversal from before the pandemic, when there were always more unemployed people than available jobs.

The July report on job openings is the first of several measures this week of the labor market’s health that the Federal Reserve will be watching closely. If clear evidence emerges that hiring is faltering, the Fed might decide at its next meeting Sept. 17-18 to start cutting its benchmark interest rate by a relatively aggressive half-percentage point. If hiring remains mostly solid, however, a more typical quarter-point rate cut would be likelier.