San Diego’s unemployment rose nearly a full percentage point in June to 10.4 percent, the highest mark for 2011, underscoring a still-struggling economy.

Last month’s jobless rate was up from a revised 9.6 percent in May, and below the June 2010 rate of 10.5 percent, according to the state’s Employment Development Department.

The unadjusted rate for California was 12.1 percent, and for the nation was 9.3 percent for the same month, according to the July 22 report.

Over the past month, the area’s nonfarm employment grew by 6,700 jobs to bring the total to 1.24 million. For the 12 months, the region’s nonfarm workforce increased by 16,300 jobs.

The sector showing the greatest strength was professional and business services, which added 6,700 jobs over the year. The biggest subgroup in that sector was administrative and support, which gained 3,600 jobs.

Four sectors showed net losses over the 12 months, led by construction, down 2,700 jobs, and government, down 2,200 jobs.

— Mike Allen