Those numbers came during a month that saw nonfarm payrolls grow by 174,000, part of a recent trend that has seen gains slow down after a quick start to the year.

In fact, job openings in April swelled to a record high, with the government's count showing 6 million positions waiting to be filled. That represented an addition of 259,000, or a 4.5 percent gain, from March, according to the monthly Job Openings and Labor Turnover Survey from the Bureau of Labor Statistics.

If the labor market has gotten a little sluggish as of late, it's certainly not because there aren't enough jobs out there.

The openings come as employers are finding a harder time finding qualified workers; hirings for the month fell by 253,000 to 6.1 million.

But the slowdown also could be because high-paying jobs are getting harder to find. The majority of the new openings came in the accommodation and food services industry, which grew by 118,000. Open government positions also increased by 39,000, but durable goods manufacturing fell by 30,000.

"If one is looking for a job, it's out there. It just may not be exactly what is wanted," Peter Boockvar, chief market analyst at the Lindsey Group, said in a note. "Bottom line, the story remains the same in that the supply of labor is not meeting the demands."

The closely watched quits rate also declined for the month, falling 111,000 to about 3 million. The number is considered an indicator of worker confidence that better jobs are available elsewhere.

Layoffs and discharges were little changed at 1.6 million.

Over the past 12 months, according to the JOLTS survey, there were 62.9 million hires while separations totaled 60.7 million, resulting in a net job gain of 2.2 million for the period ending April 30. During that time, the unemployment rate fell from 5 percent to 4.4 percent (it was 4.3 percent through May).

Much of the fall in the jobless rate has come due to a relatively low labor force participation level.

JPMorgan Chase CEO Jamie Dimon said the participation rate has been declining for men, though that also represents an underutilized part of the labor force that could be poised for growth. The rate for men aged 25 to 54 was at 88.4 percent in May, down from as high as 96 percent back in 1970.

"That is a huge number. There is something wrong," Dimon said Tuesday during a news conference for the Business Roundtable, which he chairs. "I do believe we'll get a lot of those people back in the workforce."