The survey, conducted by daily Berliner Zeitung, indicates that 21 of the 30 DAX corporations reject the idea of a mandatory quota.
Only the Munich-based insurance giant Allianz came out tentatively in favour of a mandatory quota. Eight DAX corporations declined to take a position on the debate, while the rest said they were opposed.
Only 1 in 6 executive positions (17.6 percent) at DAX corporations are currently occupied by women.
The three companies with the lowest percentage of women in top posts are industrial conglomerate ThyssenKrupp (6 percent) and the chemical companies BASF (6.5 percent) and Kali+Salz (7 percent).
Allianz, with 33 percent, is Germany's second-leading employer of executive women behind only Lufthansa, who employ 41 percent.
Karl-Ludwig Kley, chief executive of Darmstadt-based pharmaceutical company Merck, explained his company's opposition to the mandatory quota.
“It makes little business sense to bring women into executive roles for the sole purpose of satisfying a quota,” he told news magazine Focus. Regardless of gender, age and ethnic origin, Kley said, “it is imperative that people in these positions are fully qualified for an executive role.”
But Kley said his company is in favour of markedly increasing the number of executive positions filled by women worldwide, and suggested setting a global goal of 25-30 percent by 2016.