U.S. job openings slipped in December, a government report showed Tuesday, but a decline in layoffs supported views of a gradual labor market recovery.

Job openings, a measure of labor demand, eased 139,000 to a seasonally adjusted 3.1 million, the Labor Department said in its monthly Job Openings and Labor Turnover Survey.

The job openings rate — a gauge of how many jobs were still open at the end of the month — fell to 2.3 percent from 2.4 percent in November. Job openings have risen about 31 percent from their record low in July 2009.

“Despite the small decline in the headline job openings rate, the overall trend of this series still appears to be upward,” said Theresa Chen, an economist at Barclays Capital in New York. “We expect further improvement in the near term, in line with the strengthening seen in many other labor market indicators.”

Layoffs and discharges fell to 1.84 million from 1.85 million in November, reflecting declines in the private sector. Government layoffs and discharges increased in December.

The improvement in the labor market is lagging the broader economic recovery, which is gaining momentum. Government data on Friday showed nonfarm payrolls increased a modest 36,000 in January.

But other labor market indicators suggest a pick-up in hiring and the government’s household survey, from which the unemployment rate is derived, showed more people were working in January. The jobless rate dropped to 9.0 percent from 9.4 percent in December.

The decline in job openings in December was led by the private sector, where openings fell sharply in construction and manufacturing. Job openings in government increased, despite the rise in layoffs.