The unemployment rate in the Washington region fell from 5.9 percent to 5.8 percent in December, according to a report released Wednesday, as some contractors concerned about federal spending cuts picked up their hiring to bring in more business.

The federal government, long the economic engine of the Washington region, lost 3,900 positions from December 2010 to December 2011, the U.S. Labor Department reported.

Led by some growth at the local and state levels, the government gained a net of 100 jobs during that 12-month period, but 13,300 positions were created in the private sector. Professional and business services — which include government contractors as well as accountants, lawyers and other white-collar positions — added the most private-sector jobs: 8,200.

In December, “we saw more job orders than we’d seen in the previous December,” said Eric Beebe, president and general manager of MR Gaithersburg, a recruiting firm. “We saw more people hiring, more interviews and more decisions.”

Facing the threat of federal cutbacks, contracting firms are interested in hiring people who can secure contracts from the agencies that are still using consultants and from outside the government, some recruiting firms say. Beebe said contracting firms he works with have boosted hiring for positions such as as directors of business development and contract and proposal experts.

As for the public sector, given that many agencies are working with budgets that are expected to shrink over the next few years, experts say there are no prospects for a reversal of federal hiring trends soon.

“The reduction in federal jobs will continue to increase over the next few years,” said John M. Palguta, vice president for policy at Partnership for Public Service, which helps the federal government recruit job candidates. “I don’t think anybody in the federal government is expecting to add jobs.”

State and local governments, however, have made a big turnaround, said John McClain, deputy director of the Center for Regional Analysis at George Mason University. In July, the sector lost a net 8,000 jobs, but it gained a net 4,000 jobs in December. Officials from the Metropolitan Washington Council of Governments have said that several local governments have begun hiring again.

With five straight months of job growth, analysts expressed cautious optimism about the region’s prospects for a sustained recovery. The region posted a net 12-month loss of 1,900 jobs in June and 6,400 in July. The region’s net job gains since August have been steadily rising.

“I think the big-picture story is that the metro area seems to be regaining a little bit of strength as the year ended,” McClain said. Still, given the looming federal cutbacks, he said, it’s still possible for the region to start out strong and hit another bump, as it did last year.

In a new experiment, the Labor Department recently began offering seasonally adjusted unemployment rates for metropolitan regions, allowing for month-to-month comparisons. But the employment data are not seasonally adjusted, so only year-to-year comparisons of job losses and gains can be made.

Other sectors that added jobs were education and health, up 6,200; leisure and hospitality, up 5,500; and financial activities, up 600.

Sectors that lost jobs were construction, down 2,100 jobs; information, down 1,600; and retail, down 300.

The region’s unemployment level is still well below the national rate of 8.5 percent in December. Jobless rates fell in 329 of the 372 metropolitan areas across the country, according to the report. It rose in 36 areas and was unchanged in seven.

El Centro, Calif., registered the highest unemployment rate at 26.8 percent. Bismarck, N.D., posted the lowest: 3.2 percent.