Washington employers added 4,000 jobs and the unemployment rate held steady at 6.1 percent in May, according to preliminary, seasonally adjusted estimates by economists with the state’s Employment Security Department.

“This is the lowest monthly job gain so far this year,” said Paul Turek, an Employment Security labor economist. “Meanwhile, our workforce grew, but the unemployment rate stayed the same because the proportion of job seekers who got work about equaled those who did not.”

So far this year, employers have added an average of 6,560 jobs each month, which Turek said made for a solid year of job creation despite May’s modest gain.

Employment Security economists also revised their April job-growth estimate, boosting the estimated number of new jobs created from 7,700 to 8,900. Between April and May, the number of unemployed job seekers looking for work in Washington increased by about 1,600 to an estimated 211,800. That includes 74,309 who claimed unemployment benefits in May. At the same time, the state labor force of nearly 3.5 million increased by 6,500 workers.

During the one-year period ending in May, Employment Security estimates that 73,900 jobs (not seasonally adjusted) were added statewide.

In May, job growth was concentrated in the private sector, which gained an estimated 5,200 jobs overall. That was offset by a decline in overall government employment: a loss of 1,200 positions. Some of the state government jobs cut in May had been created in response to the State Route 530 mudslide, Turek said. Others were open positions that went unfilled.

Results of the latest employer survey showed job losses in eight labor-market sectors, compared with gains in five.

In May, the biggest job increases occurred in leisure and hospitality, which added an estimated 3,300 jobs. Other sectors reporting significant gains were retail trade, 2,100 jobs; construction, 1,800; financial activities, 800; and information, 200.

Besides government, the steepest job reductions were reported by employers providing professional and business services, where an estimated 1,200 jobs were lost. Within that sector, the vast majority of cuts took place in administrative and support services.

Manufacturing employment also fell, by 500 jobs, primarily in production of nondurable goods, such as food and paper manufacturing.

Employers also reported job losses in private education and health services, 400 jobs; other services, 400 jobs; wholesale trade, 300 jobs; transportation, warehousing and utilities, 100 jobs; and  mining and logging, 100 jobs.