Unemployment rates fell in the District and Maryland in September but remained unchanged in Virginia, according to a Labor Department report released Friday.

The District’s jobless rate dropped to 8.7 percent from 8.8 percent, with 14,200 jobs added. Maryland added 9,800 jobs, bringing its rate down to 6.9 percent from 7 percent. In Virginia, where 11,500 jobs were added, the unemployment rate registered at 5.9 percent for the third straight month.

In Maryland, the strongest job growth came from the professional services industry, which has long been a cornerstone of the region’s economy but has recently posted tepid growth. The state added 4,100 jobs in that sector.

“It’s a good surprise, given the issue of the ‘fiscal cliff’ hanging over the state,” said Daraius Irani, director of the Regional Economic Studies Institute at Towson University.

Virginia’s greatest gains came from the education and health services sector, a bright spot in the local economy in recent months.

Local unemployment numbers.

“That sector probably will continue to do well because of the aging population,” said Ann Lang, senior economist for the Virginia Employment Commission.

Although the jobless rate stayed the same in Virginia in September, Lang said the report was still encouraging because of the significant expansion of the state’s labor force.

The District added 11,700 jobs in government in September, a sharp jump from the 9,800 jobs that were lost in this sector in August. Ryan Price, a research associate at the Center for Regional Analysis at George Mason University, said that local- and state-level positions, not federal jobs, accounted for the increase.

After hitting a 22-year high in August, the construction sector lost 400 jobs in the District. Jobs were added in this industry in both Maryland and Virginia.

Throughout the metropolitan area, job growth slackened in the leisure and hospitality sector to the slowest rate in two years. Price said that could indicate that residents are spending less on eating out and other entertainment because of economic uncertainty.

In Maryland and Virginia, unemployment rates were significantly lower than the national rate, which dipped to 7.8 percent in September. Although the District has seen a 1.7 percent year-over-year drop in its jobless rate, it has remained higher than the national rate.

Still, Price said that job growth here trails that seen in other parts of the country.

“In terms of growth rates, we’re kind of towards the bottom of the pack,” Price said.

Jobless rates declined in 41 states, rose in six states and were unchanged in three. As it has every month since May 2010, Nevada reported the highest unemployment rate of any state: 11.8 percent. The lowest rate, 3 percent, was recorded in North Dakota.