Correction: An earlier version of this article incorrectly reported that the D.C. unemployment rate fell to 10.1 percent in January. It dropped to 9.9 percent.

Unemployment levels dropped in the District, Maryland and Virginia in January, the Labor Department reported Tuesday, bolstering a range of positive economic data suggesting that a stronger recovery is taking hold across the nation.

Virginia’s rate dropped the most among the three local jurisdictions — tumbling 0.3 point to 5.8 percent. The District’s rate dropped 0.2 point to 9.9 percent, and Maryland’s fell 0.1 point to 6.5 percent.

The unemployment rate fell in 45 states and the District and remained steady in four states. New York is the only state that recorded an increase in the jobless rate.

“What we’re seeing is a generally broad-based recovery of the economy,” said John McClain, deputy director of the Center for Regional Analysis at George Mason University. “Building permits . . . the manufacturing index, the consumer confidence index are all going up. The only thing negative [we’re seeing] in terms of national indicators is housing.”

The survey of employers showed steady gains in the professional and business services sector, especially in Virginia, which added 3,200 positions. The District reported that it lost 3,900 professional and business services jobs in January, while Maryland gained 400.

Officials at Fairfax-based IT firm CGI Federal said they hired 195 employees in metropolitan Washington in the first quarter of its 2012 fiscal year, a 49 percent increase over the same period in 2011. In the second quarter, which started in January, the company said it hired 145 workers in this area.

“What you see is a bump up in [government] awards toward the end of the year,” said Donna Ryan, president of CGI Federal. The company is ramping up for government contracts, officials said, including developing a health insurance exchange and moving computer services at the Departments of Labor and Homeland Security into the cloud.

Construction, which lost tens of thousands of jobs during the past several years, is having a revival in Virginia and Maryland. Virginia gained 4,400 construction jobs, and Maryland added 3,000.

January is traditionally “a slow month for construction jobs” in Maryland, Alexander M. Sanchez, secretary of the state’s Department of Labor, Licensing and Regulation, said in a conference call Tuesday with reporters. He attributed the uptick to the mild winter weather.

The District lost jobs in every sector, according to the city’s Department of Employment Services, which officials say is a phenomena that typically occurs in January. Still, the unemployment rate declined because the jobless rolls fell by 400 and 1,500 more residents found work in the region.

“More District residents were in jobs compared to last month,” said James H. Moore, the department’s chief economist.

Another Labor Department report released recently showed that not-seasonally-adjusted unemployment rates fell in the vast majority of the nearly 20 counties and cities encompassing the Washington region during the 12-month period ending in December 2011.

Unemployment levels from that survey ranged from 3.6 percent in Arlington County to 10.2 percent in the District.

Jobless rates rose in the District to 10.2 percent from 9.2 percent; in Fairfax City, 6.2 percent from 5.2 percent; and Falls Church, to 6.7 percent from 5.7 percent. It remained steady at 4.2 percent in Loudoun County and at 6.5 percent in Manassas Park.

In January, D.C.’s jobless level remained above the nation’s 8.3 percent unemployment rate for that month, while Virginia and Maryland stayed below it.

Nevada had the highest jobless rate in the nation — 12.7 percent. North Dakota had the lowest — 3.2 percent.