The Washington area’s unemployment rate dropped slightly to 5.4 percent in June, from 5.5 percent in May, according to a Labor Department report released Wednesday, as employers remained uncertain over how the forthcoming “fiscal cliff” would affect the jobs picture in the region.

The net gain in jobs for the region was 36,100 in the 12-month period that ended in June. The education and health services sector had the greatest gains, with 13,000 jobs added from June 2011 to June 2012.

The strength in the sector is important, because “it’s going to be one of the mainstays of the economy in the near term while there’s so much uncertainty with government activities,” said James Bohnaker, associate economist at Moody’s Analytics.

The federal government, which has typically been a strong pillar of the local economy, lost 4,000 jobs during that same one-year period. And more cuts could be coming if Congress allows planned automatic federal spending cuts to take place at year’s end.

Because of job losses in that key sector, “the Washington metropolitan area may now be positioned to grow less rapidly than the balance of the nation,” said Anirban Basu, chairman and chief executive of Sage Policy Group, an economic and policy consulting firm in Baltimore.

Still, the region’s unemployment rate is far below the national one, which held steady at 8.2 percent in June.

Analysts said Washington area businesses are in a “wait-and-see period” when it comes to hiring and layoffs as they watch how the federal budget debate plays out.

“They’re waiting to learn about capital gains tax rates, dividend tax rates and other variables that will help determine what their 2013 will look like,” Basu said.

The retail sector also shed jobs during the one-year period. Analysts said the decline was probably not caused by any factors specific to the Washington region but rather was a result of a broader pullback in consumer spending and a retreat in consumer confidence.

Still, most other sectors added jobs. Professional service jobs jumped by 6,800.

John McClain, deputy director of the Center for Regional Analysis at George Mason University, said this was probably because of growth among professions such as doctors, lawyers or engineers. ­McClain said federal contractors, which are included in that sector, would be among the employers most likely to be hesitant about hiring as the fiscal cliff looms.

Construction had an increase of 4,700 jobs, and financial activities were up 5,500. The leisure and hospitality sector added 7,100 jobs.

Although the report doesn’t signal a downturn, Bohnaker said, it does show that “businesses are more anxious and cautious about where the economy’s headed.”

Unemployment rates dropped in 328 of the 372 metropolitan areas measured in the report. Rates were unchanged in 12 areas and ticked up in 32 areas.

A Southern California city, El Centro, had the nation’s highest jobless rate (28.2 percent). North Dakota’s capital, Bismark, has the lowest unemployment rate (2.5 percent).