In another dose of bad economic news, Los Angeles County lost nearly 13,000 jobs in August as government payrolls were slashed, pushing the unemployment rate up two-tenths of a point to 12.6 percent.

The county’s August unemployment rate was slightly higher than the state’s rate of 12.4 percent and significantly higher than the national rate of 9.6 percent, according to state figures released Friday. L.A. County’s unemployment rate stood at 12.4 percent in July and 12.1 percent a year ago.

The unemployment rates for the county’s two largest cities once again topped 14 percent, with Los Angeles at 14.3 percent and Long Beach at 14.2 percent.

The county saw a drop of 12,800 non-farm payroll jobs in August, with two-thirds of those losses coming from the government sector. Local government lost nearly 5,000 jobs as budget cuts took hold, while federal government jobs fell by 2,600 as many of the remaining census workers were let go. Another 1,800 jobs were shed from the manufacturing sector.

One of the few bright spots was the construction sector, which gained 2,400 jobs in August on top of nearly 2,000 jobs gained in July. The increase signals a rebound from the sector’s three-year slump following the collapse of the housing market.

A different survey that measures the number of payroll jobs in L.A. County shows that number fell by 39,400 between August 2009 and August 2010, a drop of about 1 percent. That’s a larger year-over-year drop in jobs than the 23,500 recorded between July 2009 and July 2010.

The government sector posted the largest year-over-year reduction in jobs of 22,600, with the bulk of those coming from local government. Manufacturing employment fell by 13,300 jobs.

The entertainment sector continued its rebound, posting the largest year-over-year jobs gain of 18,000. The leisure and hospitality sector saw a slight gain of 3,600 jobs during that time period.