L.A.’s slow but steady jobs recovery continued in June as the unemployment rate fell to 11.2 percent and the county added 13,000 jobs, led by a rebound in construction, according to state figures released Friday.

The county’s unemployment rate fell last month from 11.4 percent in May, the state Employment Development Department reported. It marks the third straight month the rate has fallen and bucks the typical seasonal trend of increased unemployment as schools let out and people look for summer jobs. A year ago, the county’s unemployment rate stood at 12.4 percent.

However, L.A. County’s June unemployment rate still trailed the statewide average of 10.7 percent and was well above the national rate of 8.2 percent.

Locally, the county’s two largest cities – Los Angeles and Long Beach – posted unemployment rates of 12.2 percent.

The modest monthly increase in the county’s payroll jobs came as nine of the county’s 11 major industries reported gains. Unlike the unemployment figures, which are derived from a household survey, the payroll jobs data come from a sampling of local company payroll filings with the state.

More significantly, over the past year, the county added 57,000 jobs for a growth rate of 1.5 percent, the highest year-over-year rate in more than 12 months, indicating steady improvement in the job market.

In a welcome turnaround, the construction industry, which had been decimated by the housing bust, led the way, adding 3,700 jobs in June. Other industries with significant job gains in June included eateries, transportation and warehousing, broadcasting and professional and business services.

“We’re seeing a pickup in requests for temporary workers in these sectors,” said Mara Klug, regional vice president with the Los Angeles office of Adecco, a human resources and temporary employment company based in Zurich, Switzerland.

“Even more encouraging, about 22 percent of these temporary jobs are turning into permanent jobs, a much higher percentage than at any time since 2007. It means companies are seeing increases in their business beyond their expectations,” she said.

As is typical for June, private education posted the biggest drop in payrolls, shedding 9,200 jobs.