The unemployment rates in the District, Maryland and Virginia dipped in December, according to Labor Department data released Tuesday that also showed potential warning signs about the durability of the region’s economic recovery.

In some cases, the jobless rate is falling for the wrong reasons as local employers continue to wade through the impact of the across-the-board spending cuts known as the sequester.

Maryland added 7,300 jobs during December as its jobless rate fell to 6.1 percent from 6.4 percent in November — the lowest level in five years. But the state’s labor force also decreased slightly, suggesting that its unemployment rate may have declined, in part, because people gave up looking for work.

Maryland’s greatest job growth came from the hospitality sector, which added 2,900 jobs. That industry was consistently the chief source of job growth in the Washington region throughout 2013. The state also added 2,700 positions in the professional services industry and another 2,600 jobs in trade, transportation and utilities.

Virginia’s unemployment rate slipped to 5.2 percent from 5.4 percent. But job growth in the commonwealth was modest, with 3,100 positions added. Much of the gains came from the construction industry, which added 2,500 jobs, and education and health services, which added 1,100 positions.

But not all news was good. Virginia shed 300 professional services jobs and 900 government jobs, sectors that have typically been critical to propelling its labor market.

“It tells me we have an economy that’s still suffering from the impacts of the sequester and continuing effects of uncertainty in the marketplace. Businesses aren’t yet confident enough that they’re expanding in advance of demand,” said Stephen Fuller, director of the Center for Regional Analysis at George Mason University.

Still, Fuller and other economists have said that the uncertainty that has plagued local employers may lift soon. Now that Congress has reached a deal on the federal budget, local contractors and other companies have gained some clarity about how to steer their businesses, which economists say could boost job growth in 2014. Continued improvement in the housing market, Fuller has said, could also spark a surge in jobs in the local construction industry.

“Eventually, going into 2014, I would look for things to gradually improve — it’s just too soon for that now,” said James Bohnaker, an economist at Moody’s Analytics.

Signals about the health of the job market were mixed in the District. The jurisdiction shed 1,900 jobs overall, with its only growth coming in the government sector, which added 400 positions. Nearly every other category shed jobs, with the steepest losses coming from the education, health services and the professional services sectors.

However, the unemployment rate tumbled to 8.1 percent from 8.6 percent, its lowest level since 2008. The size of the District’s labor force also increased, a sign that the drop in the jobless rate was not likely a result of people simply ceasing to look for work.

Bohnaker said this positive change could hint that job gains are on the horizon for the District.

“Looking at it over a couple-month period, the survey that captures the unemployment rate can be a better indicator of some turning point in the jobs cycle,” Bohnaker said.

The national jobless rate edged down to 6.7 percent in December, its lowest level since 2008. However, the decrease came as the economy added just 74,000 jobs.

Unemployment rates fell in 39 states and increased in two states last month. Rates remained unchanged in nine states. With a jobless rate of 9.1 percent, Rhode Island posted the nation’s highest level of unemployment. The lowest rate, 2.6 percent, was recorded in North Dakota.