Washington’s seasonally adjusted unemployment rate increased to 9.3 percent in June, up from May’s revised rate of 9.1 percent, according to the state Employment Security Department.

The state lost an estimated 10,500 non-agricultural jobs, seasonally adjusted.

“I am confident the steps we are taking at the state and federal levels will help us pull out of the most challenging economic times since the Depression,” Gov. Chris Gregoire said. “We are beginning to see signs that our economy may be stabilizing and recovery efforts are working, but it will take time.”

Industries with the most job growth in June included leisure and hospitality, which added 500 jobs, and professional and business services, up 100. Industries with the largest declines were government, which cut 4,600 jobs, retail trade, down 2,100, education and health-care services, down 1,200, and construction, which also cut 1,200 jobs.

Year over year, Washington had 117,800 fewer jobs last month than in June 2008, a 4 percent decrease. Nationally, employment declined by 4.1 percent over the past year.

An estimated 329,983 people (not seasonally adjusted) in Washington were unemployed and looking for work in June.

“Although we are still in recession, the rate of job loss and the rise in unemployment appear to be moderating somewhat,” said Dr. Greg Weeks, who heads Employment Security’s labor-market information office.

Laid-off workers can apply for unemployment benefits online at esd.wa.gov or call 800-318-6022. When filing for unemployment, it is very important to provide complete and accurate information in order to prevent lengthy delays in processing claims.

Job seekers can get help looking for work at Employment Security’s affiliated WorkSource career centers across the state, where a variety of employment services are offered, including training programs, free help with interviewing skills or résumés, and with job referrals.

WorkSource offices and more than 12,000 current job openings are posted online at www.go2worksource.com.