US Republican-majority Michigan legislature gave final approval to "right-to-work" restrictions on public sector unions in a state considered a stronghold of organized labour, as protesters chanted in the gallery and thousands rallied outside.

The House passed the measure making membership and payment of union dues voluntary for public sector employees such as teachers by a 58-51 vote. The Senate approved the same bill last week so it will now go to Republican Governor Rick Snyder, who has promised to sign it into law.

The public sector law was the first of two expected to be approved by the House today. The other covers private sector workers, including the large auto industry in Michigan.

More than 12,000 workers from throughout Michigan and the US Midwest protested as the legislature voted, most gathered in freezing temperatures and a light snow outside the building to show their displeasure.

Michigan State Police Inspector Gene Adamczyk said the Capitol was closed to visitors when it reached capacity of 2,200. An estimated 10,000 people demonstrated outside.

A few protesters were ejected from the Capitol after they chanted slogans from the gallery during the debate. Outside of the building, protesters tore down two tents set up for supporters of right-to-work as the crowd applauded but Adamczyk said there had been no arrests by late morning.

The show of force by unionized workers recalled huge rallies in Wisconsin two years ago when Republicans voted to curb public sector unions.

The right-to-work movement has been growing in the United States in recent years. Indiana earlier this year became the first state in the industrial Midwest to approve right-to-work and several other states are watching the Michigan action closely.

Michigan would become the 24th state to enact right-to-work provisions in a stunning blow to the power of organized labour in the United States, which has suffered a series of setbacks in recent years.

Wisconsin Republicans in 2011 passed laws severely restricting the power of public sector unions. While Wisconsin did not even attempt to pass right-to-work, the success of Republicans there in curbing powerful unions such as teachers and state workers emboldened politicians in other states to follow suit.

Michigan is home of the heavily unionized US auto industry, with some 700 manufacturing plants in the state. It is also the birthplace of the United Auto Workers, the richest US labour union. Michigan has the fifth highest percentage of unionized workers in the United States at 17.5 percent.

Detroit area is headquarters for General Motors Co, Ford Motor Co and Chrysler, which is majority owned by Fiat SpA.