WASHINGTON — Company job openings fell for the second straight month in June, a sign that hiring isn’t likely to pick up in the coming months.

The Labor Department says job openings at businesses fell to 2.54 million from 2.6 million in May. Overall openings were unchanged, as government openings ticked up.

June’s total openings are 26 percent above the low point of 2.3 million in July 2009. But that’s still far below pre-recession levels of about 4.4 million openings per month.

The report suggests that slow hiring is the biggest hurdle facing the nation’s work force. Layoffs by private companies fell to just below 1.7 million, similar to the pace before the recession. Private sector layoffs rose to a peak of 2.5 million in January 2009.