Job openings fell in June, suggesting that the labor market is cooling.

The number of job openings fell for the third consecutive month in June, a sign that the red-hot U.S. labor market may be starting to cool off.

Employers posted 10.7 million vacant positions on the last day of June, the Labor Department said Tuesday. That is high by historical standards but represents a sharp drop from the 11.3 million openings in May and the record 11.9 million in March.

The job market remains strong by most measures. There were still nearly twice as many job openings as unemployed workers in June, and employers are raising pay and offering other incentives to attract and retain staff. Layoffs remained near a record low in June, suggesting that employers were reluctant to part with staff they worked so hard to hire. And the number of workers voluntarily quitting their jobs remains high, although it has fallen from last year’s peak.

The decline in openings, though modest, is likely to be encouraging news for policymakers at the Federal Reserve, who have been trying to slow down the economy in an effort to tame inflation. Jerome H. Powell, the Fed chair, and other officials have pointed to the number of vacant jobs as evidence that the labor market is too hot. They are hoping that employers will start posting fewer jobs and hiring fewer workers before they begin laying people off, allowing the job market to cool down without causing a spike in unemployment.

Still, any slowdown in the job market will mean that workers have less leverage to demand raises when pay is already failing to keep up with inflation. Slower wage growth, in turn, could lead consumers to spend less, increasing the risk that the United States could slip into a recession.

Economists and policymakers will get a more up-to-date picture of the job market on Friday, when the Labor Department releases data on hiring and unemployment in July. Forecasters surveyed by FactSet expect the report to show that employers added about 250,000 jobs last month, down from 372,000 in June.