Metropolitan Washington’s public sector, long a dependable supplier of jobs even in times of recession, appears to be facing turmoil as the region tries to find its footing in a tentative recovery.

The area’s unemployment rate rose to 5.9 percent in July, from 5.8 percent in June, according to Labor Department data released Wednesday. And the region posted a net loss of 11,100 government jobs from July 2010 to July 2011.

The Labor Department released seasonally adjusted unemployment numbers on Wednesday afternoon as part of an experiment to improve its data reporting. Earlier in the day, the agency released data that were not seasonally adjusted and that showed a jobless rate of 6 percent in July, down from 6.3 percent the year before.

A steep decline in government jobs from June 2010 to June 2011 partly reflected the loss of temporary Census Bureau employees, who ended their assignments last fall. But in the meantime, the job market was hit by a hiring slowdown in local government. The federal government accounted for only 2,900 of 11,100 jobs lost from July to July in the overall government category; the rest came mainly from local governments.

The Labor Department does not provide seasonally adjusted data on job gains and losses, which means only year-to-year comparisons are available.

Cities and counties in the region found themselves in a more-precarious situation because federal stimulus money that bolstered their budgets in recent years has run out, said David Robertson, executive director of the Metropolitan Washington Council of Governments. “Fairfax, Arlington and Prince George’s are very affluent counties, but they have been in furloughs and [job] reductions for the past two to three years,” Robertson said. Robertson added that he expects federal spending reductions and the cost of cleaning up after Hurricane Irene to put more pressure on local governments. “I don’t see how that will be a plus-plus for the national capital region,” he said.

Facing a budget shortfall this year, the District reduced the number of youth summer jobs to about 14,000, from 25,000 last year, according to the city’s Department of Employment Services.

July’s report shows public and private employment undergoing a role reversal. During the recession, governments hired steadily as private-sector employment faltered. Now the private sector is propping up the area economy as federal, state and local governments cut jobs. The region’s net job loss in the 12-month period that ended in July was 7,900, nearly three times the net loss of 2,700 jobs from June to June.

Even the most optimistic assessments of the region’s job picture showed some cracks.

JobSerf, a Dallas-based job search firm, ranked the Washington area first among 30 metropolitan areas in its index of per-capita hiring levels for August. But Jay Martin, chairman of the firm, said: “We aren’t convinced the uptick in hiring in August isn’t anything other than a backlog created by July’s uncertainty manifesting itself in early August. Washington, D.C., historically a strong city in hiring, has had some instability in being able to maintain its frenetic pace.

“We believe the desire to reduce government spending is creating pessimism.”

Another troublesome factor, analysts say, is that even growth sectors are showing weakness. Professional and business services grew by 7,900 from July to July. But that is down from 13,500 from June to June.

Government contractors, which represent a large portion of the professional and business services category, “are more cautious in hiring,” said Alan Chvotkin, executive vice president and counsel at the Professional Services Council, which represents the industry. “We’re seeing growth in spending around information technology systems, making sure everyone’s got new communications tools, before they go to hiring more people.”

Sectors that gained jobs included education and health, up 4,800 from July to July; financial activities, up 2,600; leisure and hospitality, up 1,700; and retail, up 1,200. Earlier this year, construction appeared to be poised for a turnaround as workers in their 20s and 30s move to the region for jobs and fueled the demand for apartments. Analysts were projecting that construction job gains would outweigh losses this year. But that no longer seems to be the case.Sectors that lost jobs included construction, down 6,400 from July to July; technology, down 600; and manufacturing, down 300.

The region’s jobless rate in July was well below the national rate of 9.1 percent. The unemployment rate fell in 257 of 372 metropolitan regions across the nation. It rose in 94 and remained steady in 21. Yuma, Ariz., had the highest jobless rate among the 49 largest metropolitan areas: 30 percent. Bismarck, N.D., had the lowest: 3 percent.