American employers hired 192,000 new workers in March, a sign that the job market appears to be leaving a winter chill behind.

The job gains, reported by the Labor Department on Friday, finally nudged private-sector payrolls above the level reached as a deep recession was beginning six years ago. Payroll employment is now about 100,000 jobs higher than the roughly 116 million jobs that private firms provided back in January 2008.

But the progress comes with some big asterisks.

Total US jobs are still well below their early-2008 peak, because the public sector (government) has shed 547,000 jobs over the same period. And population growth means that more Americans want to work. The result is that unemployment remains stubbornly above normal, with 2.8 million more people unemployed today than when the recession began about six years ago.

Friday’s jobs report showed a national unemployment rate of 6.7 percent, unchanged from the month before. The lack of month-over-month improvement came for what many economists see as a “good” reason: The added jobs were offset by rising participation in the labor force by people looking for work.

Another challenge ahead for the labor market: US workers are still waiting for a solid revival of wage growth after the recession.

“The only disappointment [in Friday’s numbers] is that … average hourly earnings were unchanged in March,” Paul Ashworth, chief US economist for Capital Economics, said in a report analyzing the numbers.

In theory, a better climate for wages should follow as the job market improves and employers have to compete more for worker talent. Mr. Ashworth said he expects wage growth to accelerate later in the year.

Job growth had slowed markedly in December and January, so the March figures were a welcome return to the kinds of steady gains seen through much of last year. For March, government employment in the US was unchanged, so 192,000 was the hiring total for both the private sector and for the overall economy.

The Labor Department also revised upward an earlier estimate of February job gains to 197,000. Together with a January revision (up to a still-modest 144,000 jobs for that month), those upgrades added another 37,000 in job gains, compared with estimates as of last month.

The recession was so deep that the number of private-sector jobs fell dramatically – reaching a low of 107.2 million by the end of 2009 – and has recovered more slowly than usual.

Despite the arrival of new jobs to fill that gap left by the recession, the labor market recovery still has a long way to go. Because of a decline in public-sector jobs, total US employment is still 437,000 below the peak reached in January 2008.

And the number of Americans wanting to work is also larger now than it was back then, by about 2.2 million people.

Wages are one piece of evidence that the job market still has a lot of what economists call “slack” – meaning unused productive capacity and more available workers than jobs.

Hourly pay is essentially the same today as it was when the recession officially ended in June 2009, when measured for all private-sector workers and adjusted for inflation. That’s because meager pay gains have barely kept pace with inflation.

The recent trend line seems to be moving in a positive direction, though.

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Real wages (adjusted for inflation) dipped during the early phase of the economic recovery but have been at least edging upward modestly since late 2012.

Many economists expect wage growth to pick up slowly. Forecasters in a March survey by the National Association for Business Economics said that, after real pay rose just 0.2 percent last year, employers should boost real compensation by about 0.4 percent this year and 0.7 percent next year.