Union membership in the U.S. workforce has withered to its smallest share since the 1940s.

Just 11.3 percent of wage and salary workers were union members in 2012, down from 11.8 percent in 2011, the U.S. Bureau of Labor Statistics reported Wednesday.

Union membership fell by nearly 400,000 workers, to about 14.4 million.

More than half the decline came in the public sector as Republican-led states such as Wisconsin, Indiana and Michigan stifled bargaining rights for public employees.

Other states substantially cut government payrolls, and some are considering joining nearly half the states that have “right to work” laws prohibiting unions from requiring workers to pay dues as a condition of employment.

Unions last year represented 36 percent of public employees, such as teachers, police, firefighters and government-agency workers, down from 37 percent a year earlier.

Losses also grew in the private sector, as union membership slipped to 6.6 percent from 6.9 percent of employees.

Furthermore, most job growth nationally — as modest as it was — occurred in nonunion companies.

The tough year for organized labor is prompting many unions to try to rally their members.

Unions around the country are joining coalitions such as Jobs for Justice to augment their advocacy for broader wage and hour issues, such as minimum-wage increases.

“Most in the general public see only negative stories about unions and don’t understand that we’re the ones who have negotiated workplace standards over the last century,” said Dave Wilson, business agent for the Carpenters’ District Council in Kansas City, Mo.

Union membership peaked in the 1950s, when about 1 in 3 U.S. workers belonged to a union. By 1983, the union share was down to about 1 in 5.

Most people appreciate what collective bargaining produced historically, but they don’t look as favorably on unions today.

A Gallup poll last year found that 52 percent of the American public approved of labor unions, up slightly from the survey’s historic low of 48 percent in 2009.

“There’s a real slowing off in organizing,” said Judy Ancel, director of the Institute for Labor Studies at the University of Missouri, Kansas City.

That doesn’t mean unions are dying, she said. Instead, they’re throwing their influence into politics and social-justice issues by building coalitions with other groups.

“There’s been a ceaseless, hammering attack against unions since Ronald Reagan fired the air traffic controllers in 1981,” Ancel said. “The word ‘union’ scares people because they’ve been bludgeoned to think unions are old-fashioned, corrupt money-grubbers. Yet people want raises. They want pensions. They want the rights to a hearing if they’re fired. They want the things that unions can give them.”

Much of what unions fought for in the past “has now been codified into federal law,” countered J. Justin Wilson, managing director of the Center for Union Facts, an organization funded by corporations, foundations and individuals.

“So the bargaining power of unions comes down to wages, and companies are saying it’s just not feasible to continue to pay more,” Wilson said.