The state’s unemployment rate remained at 8 percent for the fourth consecutive month in May despite modest job gains, the Department of Labor reported Thursday, citing mixed signals about the future of Connecticut’s job market.

And the state’s largest health insurance company announced plans Thursday to add jobs in south central Connecticut later this summer.

The May job gain — about 1,000 non-farm positions — coupled with 5,400 jobs added in April, marks the best five-month start the labor market has enjoyed since it began climbing out of the recession in 2010.

“With the exception of a storm impacted February, Connecticut has been experiencing consistent job growth so far this year,” said Andy Condon, director of the department’s Office of Research. “The upward turn in labor force participation, after 35 straight months of decline, may indicate increased confidence in labor market conditions.”

Connecticut now has regained 58,600 jobs, or 48 percent of the 121,200 jobs it lost in the recession between March 2008 and February 2010.

But Condon quickly added that, “there are still headwinds ahead.”

Federal budget cuts ordered as part of the sequestration effort “could hinder employment growth possibilities throughout the rest of 2013,” he said.

A mechanism designed to limit the size of the federal budget, sequestration places a hard cap on spending in several broadly defined areas. If Congress appropriates funds in excess of these caps, it automatically triggers across-the-board cuts in all affected categories.

In this case, Congress exceeded limits set in the Budget Control Act of 2011, triggering $984 billion in total cuts between 2013 and 2021.

Much of the first wave of reductions, about $85 billion, is expected to hit states as the federal fiscal year nears its close Sept. 30.

Connecticut’s May job gains were offset, though, by more than 4,000 additional state residents seeking employment.

The jobless rate reflects the number of employed workers as a percentage of the labor force — the sum of those with jobs and those on record as looking for jobs.

Four of the state’s major industry super-sectors posted job gains in May, led by professional and business services, which added 2,300 jobs.

Another growth area was education and health services, which was up 1,700 jobs, and could be poised for more growth this summer.

Anthem Blue Cross and Blue Shield announced Thursday that it is adding as many as 100 jobs at its Wallingford headquarters.

The new jobs include entry-level call center and managerial positions. Workers will handle member service activity for the eastern part of the country.

In a statement, Anthem President David R. Fusco said the positions are intended to help members “get the most out of their Anthem benefits” and better navigate changes in the health care system.

“The Connecticut workforce is ideal for expanding our capabilities to better serve our members,” he said.

Spokeswoman Sarah Yeager said the company expects the hiring to be completed by late August.

“We have a talented workforce at Anthem and in Connecticut,” she said. “The company saw the talent and made the determination to invest in the local workforce.”

“Anthem has been a strong partner over the years — employing Connecticut residents, providing great customer service and delivering high quality healthcare to thousands of businesses and families,” Gov. Dannel P. Malloy said in a statement released by his office. “Any time a company like Anthem, one that is on the leading edge of its industry, grows and expands in Connecticut, it not only raises our profile but demonstrates to others that our state is a great place to invest, live, work and do business.”

The labor department also reported gains Thursday in the trade, transportation and utilities and other services sectors.

Five of the 10 super-sectors lost ground, with government shedding the most jobs, down 1,400 positions. Manufacturing, finance and insurance, leisure and hospitality, and information also lost jobs.

The construction and mining super-sector largely was unchanged.

The labor department did not release regional and town employment data for May Thursday, but indicated it would be reported Friday.