BERLIN — Germany’s coalition government pledged Wednesday to introduce a bill mandating quotas for women on the supervisory boards of the country’s top companies, after a feud erupted this week when a leading conservative lawmaker told the minister of family affairs, a woman, to “stop whining” about the proposal.

Chancellor Angela Merkel, who is widely seen as the world’s most powerful woman but is ambivalent about compulsory quotas, pledged this fall that they would be introduced, sweeping aside criticism from a coalition party, the Christian Social Union, that the move would be costly and hurt German companies at a time when economic growth was slowing.

Ms. Merkel’s government, composed of center-right and center-left parties, called for quotas in a lengthy coalition agreement last year. Nevertheless, Germany has yet to join eight other European Union countries, including France, Italy, Spain and the Netherlands, in adopting quotas for women on corporate boards.

Ms. Merkel said a bill requiring that women make up at least 30 percent of the nonexecutive members of each supervisory board, beginning in 2016, will be introduced in Parliament on Dec. 11, where it is virtually assured of passage. The law would cover about 100 companies.