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WASHINGTON — The nation’s union membership held steady at 11.3 percent last year, but losses among state and government workers suggest an ominous trend for the future of organized labor.

In a turnabout, there are now slightly more union members working for private firms than in government, the Bureau of Labor Statistics reported Friday. That reverses a five-year trend.

Although the rate of membership among all workers didn’t budge, the overall number of union members grew slightly, rising about 162,000 to nearly 14.5 million.

Unions added about 282,000 new members in the private sector as the economy improved. But that was partly offset by the loss of 118,000 members in the public sector, as state and local governments and public school districts continued to face financial pressure from shrinking budgets.

For decades, the growth of union workers in government has helped compensate for steep losses in manufacturing, construction and other private industries where unions once thrived. The public sector union membership rate of 35 percent remains more than five times higher than that of private sector workers, at 6.7 percent.

But budget pressures have meant layoffs and hiring freezes for many state and local governments. Public unions have also been on the defensive in Wisconsin, Michigan and other states where Republican governors have pushed measures to limit union bargaining rights. In Wisconsin, union membership in the public sector fell from 53.4 percent in 2011 to just 37.6 percent in 2013.

“This suggests that the erosion of public sector union coverage reflects the new anti-collective bargaining policies implemented in several states,” said Lawrence Mishel, president of the liberal-leaning Economic Policy Institute.

The overall rate of union membership has been steadily declining for decades. The share of workers belonging to unions peaked in the 1950s at about 30 percent, and dropped to about 20 percent by 1983.