The state of Connecticut lost 3,600 jobs in August and the unemployment rate held steady at 6.6 percent, according to the Connecticut Labor Department.

It also revised downward its July numbers by 1,000 jobs. It had previously reported a gain of 2,400 positions that month.

But it’s not all bad news.

The core private sector, which makes up about 86 percent of Connecticut’s nonfarm employment, added 400 positions, while the public sector — specifically the local government subcomponent — lost 4,000 jobs or 2.6 percent. The private sector has now added 13,000 jobs this year.

“Despite the overall nonfarm job decline last month, Connecticut’s private sector continued to add jobs,” Andy Condon, director of the Labor Department’s Office of Research, said. “This summer appeared to be the best economically since the recovery began in 2010.”

Condon said the lull in employment may be due to an early sample in August before educators returned to their classrooms. The biggest job losses in August came from the local government sector.

Economist Don Klepper-Smith said the number that really matters is the year-to-date total, which shows nonfarm employment has risen only 0.5 percent for the first eight months of the year, which is below the long-term annual rate of 1.2 percent.

“This one statistic, more than any other employment metric, tells the story about Connecticut job growth. In a word: lackluster! The good news is that we’re is positive territory, but not by much,” Klepper-Smith said Thursday.

Connecticut Business and Industry Association Executive Vice President Joseph Brennan said the report contained “mixed news.”

“We’re on track to gain 15,000 jobs this year, which is an improvement, but it shows that the Connecticut economy still has a long way to go,” Brennan said.

Connecticut has regained 59.9 percent of the jobs it lost during the recession. That’s lower than the national figure of 108.6 percent.

The politicians all wanted to spin the numbers Thursday.

Democratic Gov. Dannel P. Malloy, who is in a tough re-election battle, tried to put a positive spin on the numbers.

“For the seventh consecutive month, we are seeing the private sector do what we need it to do — add jobs,” Malloy said in a statement. “The unemployment rate is at a 5-year low, and we’ve added nearly 60,000 private sector jobs since 2011. All of these are positive signs of progress but we still have more work to do. I’ve said it before, but I’ll say it again — until every resident who wants a job has one, our work is not done.”

But Republican Party Chairman Jerry Labriola called Malloy’s statement a “desperate attempt to get re-elected.”

“The fact is that Connecticut lost 3,600 jobs in the month of August — the governor can try to spin that however he wants but numbers don’t lie,” Labriola said. “Dan Malloy can claim that he’s ‘making progress’ and that Connecticut’s economy is in great shape as many times as he wants, but that won’t make it true.”

EDITOR’S NOTE: This story has been updated to include a link to the August labor situation report and more detail on the decrease in public sector employment.