“The payroll number is well above expectations,” said Jim O’Sullivan, chief United States economist for High Frequency Economics. “But the wage numbers are certainly weaker than expected, so it keeps alive the whole debate about the relationship between slack and inflation and how far the Federal Reserve should allow the unemployment rate to fall.”

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A broader measure of unemployment, including discouraged workers and those who are working part time but prefer full-time work, inched up to 8.6 percent in June from 8.4 percent in May. Still, that figure is a point lower than it was this time last year.

“It’s pretty clear that the trend in employment growth is strong enough to keep the unemployment rate trending down,” Mr. O’Sullivan said.

Diane Swonk, founder of DS Economics in Chicago, said the increase in professional jobs reflected hiring of new graduates. “Finally the millennials are getting more jobs,” she said.

Hiring in the service sector was also strong. The retail, manufacturing and construction sectors were weak, Ms. Swonk added, but the “economy looks strong enough to absorb these workers elsewhere.”

The Background

June marks the eighth anniversary of the recession’s end, when the economy hit bottom, with employers shedding hundreds of thousands of workers and the jobless rate more than double what it is today.

President Trump got ahead of the Labor Department’s release and started off the week with boasts on Twitter about the economy’s impressive performance.

He followed up with another Twitter message the next day.

As a candidate, Mr. Trump repeatedly rejected the government’s monthly estimates as phony. Now in the Oval Office, he has embraced those same reports as evidence of his administration’s success.

As he noted, the jobless rate has gone down this year, from 4.8 percent in January. Economists agree that at least some decline is natural after eight years of expansion in the monthly averages, although June exceeded those expectations. About 100,000 new jobs are needed to keep up with growth in the population. Anything beyond that will further chip away at the jobless rate or bolster the size of the labor force as workers who dropped out are lured back.

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The Search for Workers

Corporations and small establishments across sectors complain that they cannot find enough people to hire. Still, wage growth has disappointed.

“This is not a market we have typically seen,” said Michael Stull, senior vice president at the staffing company Manpower North America. “We have not before seen unemployment drop, low participation rates and wages not move. That tells you something’s not right in the labor market.”

The question is what.

Mr. Stull said employers were aware of the shrinking pool of workers and were rethinking traditional qualifications like length of experience. “Employers will take on hard-working, reliable workers even if they don’t have an opening,” he said.

At the same time, workers “are pushing back a little bit about driving an hour for a $10-an-hour job at a distribution center on the outer rim of the city,” he said. “You need a car for that, and you can’t have a car on $10 an hour.”

That’s a familiar problem to Tom Thompson, owner of Star Cleaning Systems, in Columbus, Ohio. He is looking to add two or three part-time workers to his 20-member staff. As Mr. Thompson said, “If you don’t have a car in suburban America, you can’t work.”

At the same time, “very few people show up for interviews, and if they do, they don’t show up for the job,” he said. “I’m spending 80 to 90 percent of my time recruiting. I triple-book appointments for interviews, and I’m lucky if I get one person to show up.” He is offering $9.25 an hour to start, with bonuses and increases for workers who stick around. As the owner of a new company, he said, he cannot afford to pay significantly more.

Nearby distribution centers for big companies like Amazon are sucking up most of the available labor, Mr. Thompson said. “I sometimes wish there was actually a higher unemployment rate,” he said.

Like Star Cleaning, Rooforia Home Exteriors in Omaha often finds customers through Thumbtack, an online marketplace for hiring people to complete tasks. These days it’s the workers who are tougher to find.

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“We did everything we could to recruit people and had not one application,” Rooforia’s owner, Sarah M. Smith, said.

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She is depending on guest-worker visas to fill openings for the season, which runs from the spring through November.

“It’s hard work in Nebraska,” Ms. Smith said, “We have hot summers, and you’re on a black asphalt roof.”

At $17 an hour, she said, “the pay is fair.”

Ms. Smith said she had asked herself why it was so difficult to find American residents to fill jobs that do not require any specialized training.

“We had one person we recruited; he didn’t even show up the next day,” she said.

“We get a lot of people saying the visa program is taking jobs away from Americans,” Ms. Smith added, “but in reality, they’re not taking the jobs because there is no one even willing to do the jobs.”

Continuing Puzzles

Economists assume that an increased demand for labor should drive up wages, but that supposedly ironclad link is turning out to be much more elastic. Hourly wage growth has plodded along at an annual rate of roughly 2.5 percent in recent months, but even that number is misleading, because most of the gains have gone to more highly skilled workers, said Robert Frick, corporate economist at Navy Federal Credit Union.

“Fifty to 60 percent of lower-tier wage earners are earning less and less year over year,” Mr. Frick said. He dismissed concerns about inflation articulated by some members of the Federal Reserve, arguing that there is little evidence to show that the economy is heating up and that interest rate increases are needed.

“If the Fed starts tightening, then you’ll squeeze off wage increases that haven’t happened yet,” he said.

Matching willing employees to jobs takes time, Mr. Frick said, because unlike some European countries, the United States lacks an infrastructure for training and development that could funnel, say, would-be welders into a training program and then a job.

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Patrick Bass, chief executive of Thyssenkrupp North America, part of a German multinational conglomerate, said his company had been increasingly relying on methods common in Germany like apprenticeships, partnerships with colleges, and internships. In their plants in Ohio, Illinois and Indiana, even less-skilled jobs can take as long as three months to fill, he said, while technical and engineering positions can take six months.

“We’re willing to invest in the people and bring them in and train them,” Mr. Bass said. “But for the basic skill job, we’re seeing a higher turnover rate than normal. People are job shopping a bit, because they can. They’re trying different things to see what they like.”

Martha Ross, a fellow at the Metropolitan Policy Program at the Brookings Institution who has studied the jobless data in depth, said official statistics offered a sky-high perspective, while hiring was local.

“Even in an era of low national unemployment, with recent jobs reports showing the national unemployment rate ticking down close to 4 percent, jobs are not always available and not everyone who wants work can find it,” she wrote on her blog. “There is no one-size-fits-all approach to help people prepare for and find jobs.”

A slowdown in automobile sales this year, for example, has already prompted some automakers and dealers to pare their work forces after significant expansions.

The Washington Factor

Reviews of the economy tend to reflect political affiliations, with Republicans more optimistic since the election than Democrats. The data, however, points to a remarkably consistent story line in recent years: steady but slower-than-hoped-for progress that has tended to lift the fortunes of more highly skilled workers in urban centers and leave others behind.

“Payrolls are very volatile month-to-month, but in general, the so-called hard numbers have probably not changed all that much in the last year,” said Mr. O’Sullivan of High Frequency Economics. The employment rate has been inching down, while economic growth over all has remained tepid.

As Mr. Stull, of Manpower North America, put it: “The job market is like driving on a Friday afternoon in the summer. We keep moving forward but not nearly as fast as we’d like to.”

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Much of Mr. Trump’s pro-business agenda remains stalled in Congress. Although Republicans control the White House and both legislative chambers, they have so far been unable to agree on a final budget, a new health care plan, a tax overhaul or an infrastructure program.

“This is an unprecedented level of political uncertainty,” said William E. Spriggs, chief economist for the A.F.L.-C.I.O. “That is creating a drag on the economy.”

Mr. Spriggs noted, for example, that hiring in nursing care centers and medical labs has been dropping, which he argues is a reflection of the confusion surrounding proposed changes to the health care system.

There is a ripple effect. Juanita Duggan, chief executive of the National Federation of Independent Businesses, said, “Small-business owners seem to be in a holding pattern while they wait to see what Congress will do with taxes and health care.”