Hawaii’s unemployment rate remained at 6.3 percent in May, the state Department of Labor and Industrial relations reported Thursday.

The state’s jobless rate had been inching down since peaking at 7.1 percent during the 2008-2009 recession, but remains well above the cyclical low of 2.5 percent in 2006.

Most economists expect further improvement in the state’s job market will be gradual as the economy slowly strengthens. The University of Hawaii Research Organization is forecasting the unemployment rate will decline to 6.1 percent this year, helped by a modest 1.5 percent gain in the number of payroll jobs.

There were 41,400 people looking for work in Hawaii in May out of a total labor force of 654,000, according to the report from the state DLIR. That compared with April, when the number of job seekers totaled 41,300 in a workforce of 655,700. April’s unemployment rate also was 6.3 percent.

The slow improvement in the job market has been accompanied by a decline in the number of people filing claims for unemployment benefits. The number of unemployment claims has averaged 1,930 per week since the start of the year, down from about 2,500 a week in 2009.

Nationally, the unemployment rate rose to 8.2 percent in May from 8.1 percent in April.

The state and national jobs data are adjusted for seasonal variations, such as an influx of students into the workforce when the school year ends.

County jobless rates are not seasonally adjusted. The rate for Honolulu rose to 5.6 percent in May from 5.3 percent in April.

The rate rose to 6.7 percent from 6.4 percent in Maui County, to 8.1 percent from 7.7 percent in Kauai County and to 8.8 percent from 8.6 percent in Hawaii County.

The unemployment rate is based largely on a telephone survey of households. A separate survey of businesses showed that the number of nonagricultural jobs fell to 598,000 in May, a 3,200 net decrease from April.

Government jobs contracted by 4,000 in May, while professional and business services lost 800 positions. Construction jobs fell by 300 and manufacturing lost 100 positions. The two sectors with the largest job gains were leisure and hospitality, and trade, transportation and utilities, which added 500 positions each.