The number of U.S. job openings hit a new high in April while hiring slowed, a sign that employers are struggling to find workers.

The number of job openings rose by 259,000 to 6.04 million, the Labor Department said Tuesday, the highest level recorded since the government started tracking the figure at the end of 2000. The number of hires, meanwhile, fell by 253,000 to 5.05 million in April.

“The...