The United States has also seen women’s representation grow slightly, up to 17 percent of board seats, without legislative mandates, though its growth has been extremely slow.

The notion of government quotas for company boards has met widespread resistance in the United States. Instead, advocates have been going about it in other ways. Last year, two dozen major American companies opened a branch of the 30% Club in the United States to press businesses toward the 30 percent goal. In Silicon Valley, companies like Twitter have added a female director after criticism of their all-male boards.

Yet many American companies stop after appointing a woman or two to the board without pushing toward a particular percentage, said Ilene H. Lang, a senior adviser at Catalyst, a nonprofit research firm on women in business. Other advocates, led by Sheryl Sandberg, the Facebook executive and author of “Lean In,” are focusing less on boards of directors and more on promoting women and adopting family-friendly policies companywide.

The European Union has considered measures to mandate that up to 40 percent of corporate supervisory boards be made up of women. While they were not passed, the debate brought further attention to boardroom equity.

“I cannot reiterate enough how difficult it is for women to push this issue,” said Avivah Wittenberg-Cox, a London-based expert on building gender equality in business. Ideally, she said, such a remedy is endorsed by men; in Norway it was a male conservative minister who first pushed quotas in 2008, she said.

Friday’s vote in Germany means that “Europe is really going pretty wholeheartedly along the quota line,” she said.

The measure faced strong resistance from conservatives and from others who argued against imposing a law, despite the failure of a voluntary system that was adopted — under duress — by German businesses in 2001.