The Bay Area added 5,600 jobs in June, an upswing led by a robust tech sector in Santa Clara County and strong gains in the San Francisco-San Mateo-Marin region, according to a state government report released Friday.

The job gains improved the unemployment rate throughout the Bay Area, according to an analysis by Beacon Economics of the state Employment Development Department report.

The jobless rate in June was 5.3 percent in Santa Clara County, down from 5.5 percent in May; 5.7 percent in the East Bay, down from 5.9 percent; and 4.1 percent in the San Francisco metro area, down from 4.4 percent, according to the Beacon analysis. The unemployment rate and the job trend numbers are derived from different surveys and can move in different directions in the same month.

“The drivers of the Bay Area economy are still in place, both in Santa Clara County and the San Francisco metro area,” said Jordan Levine, director of economic research with Beacon. “Demand is still rising for technology services and products, business investment is continuing, there is still demand for capital goods. Those drivers are still poised to create job growth in the Bay Area.”

California added 24,200 jobs in June. The statewide unemployment rate fell to 7.4 percent, down from 7.6 percent in May.

Primarily because of large job losses in the government sector, which suffered employment reductions due to seasonal school-related furloughs, Santa Clara County lost 900 jobs in June. Private-sector gains came in tech-oriented industries such as professional, scientific and technical services, which added 500 jobs, and the information industry, which gained 100 jobs. Health care added 700 jobs in June.

The San Francisco-San Mateo-Marin region gained 8,100 jobs, mostly in the hotel and restaurant sector and in administrative support.

The East Bay lost 900 jobs. One of the weakest sectors was construction, which lost 1,000 positions during June. The numbers were adjusted for seasonal changes.

Despite the losses in some areas, economists agreed that the overall trend remains strong for the Bay Area.

“Every indication we see points to the jobs recovery starting to spread to other parts of the Bay Area such as the East Bay,” said Stephen Levy, director of the Palo Alto-based Center for Continuing Study of the California Economy.

The statewide economy also achieved a key benchmark during June. California now has recovered all of the jobs it lost during the most recent recession and has returned to its peak levels of 2007.

“This is significant,” Levine said. “It is a watershed mark for California.”

Contact George Avalos at 408-859-5167. Follow him at Twitter.com/georgeavalos.